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HOUGHTON,  MIFFLIN  AND  COMPANY, 

BOSTON  AND  NEW  YORK. 


THE 
SOLAR  SYSTEM 


DELIVERED  AT  THE  MASSACHUSETTS 

INSTITUTE  OF  TECHNOLOGY 

IN  DECEMBER,  1902 


BY 


PERCIVAL   LOWELL 

NON-RESIDENT  PROFESSOR  OF  ASTRONOMY  AT   THE 
MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY 
AND  DIRECTOR  OF  THE  LOWELL  OBSER- 
VATORY, FLAGSTAFF,  ARIZONA 


BOSTON    AND    NEW    YORK 
HOUGHTON,  MIFFLIN  AND  COMPANY 


1903 


Copyright,  1903, 
BY  PERCIVAL  LOWELL, 

ALL    RIGHTS    RESERVED 


Published  May,  fgoj. 


CONTENTS 

CHAP.  PAGB 

I.  OUR  SOLAR  SYSTEM i 

II.  MERCURY 27 

III.  MARS 47 

IV.  SATURN  AND  ITS  SYSTEM 72 

V.  JUPITER  AND  HIS  COMETS 94 

VI.  COSMOGONY n6 

ELEMENTS   OF  THE   SOLAR   SYSTEM 

TABLE 

I.  ORBITAL  ELEMENTS facing  134 

II.  BODILY  ELEMENTS Joeing  134 


ERRATA. 


Page  23,  line  8. 


„                 m 
Por rn    read 


Page  74,  line  18. 

For  Pierce  read  Peirce. 
Page  104,  second  line  under  diagram. 

For  P  read  O. 
Page  123,  line  i. 

After  momentum  insert  projected  at  right  angles 
to  it. 


154155 


Copyright,  1903, 
BY  PERCIVAL  LOWELL, 

ALL    RIGHTS    RESERVED 


Published  May,  igoj. 


J?. 


CONTENTS 

CHAP.  PAGE 

I.  OUR  SOLAR  SYSTEM i 

II.  MERCURY 27 

III.  MARS 47 

IV.  SATURN  AND  ITS  SYSTEM 72 

V.  JUPITER  AND  HIS  COMETS 94 

VI.  COSMOGONY 116 

ELEMENTS   OF  THE   SOLAR   SYSTEM 

TABLE 

I.  ORBITAL  ELEMENTS facing  134 

II.  BODILY  ELEMENTS Joeing  134 


! 54155 


LIST   OF   ILLUSTRATIONS 

PACK 

INNER  PLANETS 4 

OUTER  PLANETS 5 

DIAGRAM 7 

METEOR  STREAMS 14 

CONSPICUOUS  COMETS 19 

MERCURY  —  TRIAD  OF  DRAWINGS  ....  30 

LIBRATION  IN  LONGITUDE 31 

PERTURBATIVE  ACTION  —  EXEMPLIFYING  THE  ORIGIN 

OF  THE  TIDES 36 

MAP  OF  MARS 57 

DRAWINGS  SHOWING  IDENTITY  BETWEEN  CANALS  AND 

RIFTS  IN  THE  POLAR  CAP 63 

SATURN'S  RINGS 79 

POSITION  OF  MASSES  IN  SATELLITE  SYSTEMS  .  .  85 
INCLINATIONS  OF  SATELLITE  ORBITS  TO  PRIMARY'S 

EQUATOR 87 

JUPITER'S  FAMILY  OF  COMETS 100 

RELATIVE  ORBITS 104 

ACTION  OF  JUPITER 107 

COMET  APHELIA 114 

DIAGRAM 123 

FAYE'S  LAWS  OF  ATTRACTION  IN  CONDENSING  NEBULA  125 
SUCCESSIVE  CURVES  OF  ATTRACTION  IN  CONDENSING 

NEBULA 126 

DIAGRAM 127 

Axis  INCLINATIONS  OF  THE  MAJOR  PLANETS  .  .  131 


THE  SOLAR  SYSTEM 


THF"         \ 

{    UNIVERSITY    1 


\£X 


THE    SOLAR   SYSTEM 


OUR   SOLAR    SYSTEM 

IN  the  long  perspective  of  knowledge,  which  Its  position  in 
begins  with  the  close  at  hand  and  stretches  to  the  knowledge!" 
infinitely  remote,  the  solar  system  marks  a  middle 
distance.     Between   the   intimacy   possible   with 
objects  on  this  Earth  and  the  distant  recognition 
of  the  universe  of  suns,  it  furnishes  an  acquaint- 
anceship combining  something  of  the  interest  of 
the  one  with  the  grandeur  of  the  other. 

Our  knowledge  about  the  solar  system  has  its  constitu- 
greatly  increased  during  the  last  quarter  of  a  cen- 
tury ;  and  first  in  the  recognition  of  what  makes 
part  of  it.  To  our  solar  system  we  now  know 
belongs  every  heavenly  body  we  see  except  the 
fixed  stars  and  the  nebulae.  Not  only  are  the 
Sun,  Moon,  and  planets  members  of  it,  but  me- 
teors, shooting-stars,  and  comets  we  have  found 
to  be  so,  too.  That  all  of  these  bodies  are  part 
and  parcel  of  what  the  Sun  controls,  I  shall  first 


The  Solar  System 


proceed  to  show  you ;  for  it  is  proper  that  we 
should  recognize  the  members  of  the  system  be- 
fore considering  the  system's  constitution  and  the 
several  characters  of  its  constituents. 

obsolete  In  many  text-books  you  shall  find  it  still  stated 

that  these  flaming  portents,  the  cometae  or  long- 
haired stars,  —  for  the  ancients  saw  tresses  where 
we  prosaically  see  tails,  —  one  of  which,  on  the 
average,  startles  a  generation  into  wonder,  are 
visitors  to  us  from  other  stars.  So  also  we  were 
taught  that  the  strange  stones  that  fall  to  us  from 
the  sky,  and  we  call  meteorites,  were  bits  of  some 
body  from  far  interstellar  space.  Such  knowledge 
belongs  now  to  the  history  of  science,  not  to  sci- 
ence itself  ;  for  these  bodies  carry  with  them  their 
badge  of  membership  :  it  shows  in  the  orbits  they 
describe.  So,  when  we  pass  through  a  comet's 
tail,  or  pick  up  a  piece  of  meteoric  iron,  we  now 
recognize  that  we  have  to  do,  not  with  a  stranger, 
but  with  our  own  kith  and  kin.  Man  may  gaze 
at  matter  beyond  the  solar  system,  but  man  has 
never  yet  touched  it. 

Path  the  Proof  of  community  lies  in  the  character  of  the 

proof  of  one- 
ness, paths.     Planet    and    particle   alike    turn    out    to 

travel  in  ellipses,  and  ellipticity  betrays  association. 
How  the  orbit  labels  the  occupant  we  shall  see, 
on  finding  the  paths  the  planets  pursue  and  why 


Our  Solar  System 


they  pursue  them.  The  orbits  of  the  planets  are 
then  the  first  point  to  consider. 

To  begin  with  the  Sun.     Observation  shows  not  Earth  travels 

...          in  an  ellipse. 

only  that  the  Sun  changes  its  place  in  the  hea- 
vens, but  changes  its  size  as  well.  To  measure- 
ment through  a  smoked  glass,  it  seems  to  contract 
in  summer  and  expand  in  winter.  Plotting  the 
directions  it  successively  takes  in  the  form  of  a 
spider,  and  taking  the  legs  inversely  proportion- 
ate to  the  diameters  at  the  times,  we  find  an 
ellipse,  in  one  of  whose  foci  lies  the  Sun.  The 
Earth,  then,  goes  round  the  Sun  in  an  ellipse. 

To  find  the  path  of  a  planet,  we  first  get  its  So  do  the 

, .  .    ,  .    ,      .  ,  ,  10         other  planets, 

synodic  period,  or  period  with  regard  to  the  Sun. 

Then,  from  a  sufficient  number  of  observations  of 
synodic  periods  to  give  their  mean,  we  obtain  the 
sidereal  period,  or  period  with  reference  to  the 
stars. 

By  considering  the  angular  motions,  the  two 
periods  are  easily  seen  to  be  connected  by  the  fol- 
lowing equation  :  — 

i  _  i        i 
S  ~  T  ~E"' 
Where  E  =  the  Earth's  period  ; 

S  =  the  Planet's  synodic  period ; 
P  =  the  Planet's  sidereal  period. 

From   two   bearings    separated   by   a   sidereal 


The  Solar  System 


period,  we  get  a  quadrilateral,  of  which,  knowing 
parts  enough  to  solve,  we  derive  the  planet's  dis- 
tance from  the  Sun  at  the  moment.  We  now 


Distance  to 

Nearest  Fixed  Star 

275  000  A  U. 


MARS 


Distance  to 

Boundary  of  Sun's  Domain 
114000  A.U. 


FIG.  I.     INNER  PLANETS. 


Our  Solar  System 


Distance  to 

Nearest  Fixe.d  Star 

275000  A  U. 


NEPTUNE 


Distance  to 

Boundary  of  Sun's  Domain 
II4000A.U. 


FIG,  II.    OUTER  PLANBTS. 


have  for  the  planet  what  we  had  for  the  Sun,  — 
direction  and  distance  at  a  given  time.  Dotting 
these  data  upon  the  apparent  path,  Kepler  proved 


6  The  Solar  System 

that  the  orbit  of  Mars  was  an  ellipse.  Mars  was 
the  first  of  the  planets  thus  to  have  its  orbit  found ; 
following  it  the  others  yielded  similarly  to  the 
genius  of  the  man.  All  the  planets,  then,  move 
in  ellipses  about  the  Sun. 

Thus  we  have  obtained  the  accompanying  plan 
of  the  system. 

Kepler's  laws.  Kepler  discovered  two  more  relations  :  first, 
that  the  radius  vector  of  any  planet  swept  over 
equal  areas  in  equal  times ;  and,  second,  that  the 
cubes  of  the  major  axes  of  the  orbits  of  any  two 
planets  were  as  the  squares  of  their  periodic  times. 
The  latter  is  not  exactly  true,  but  becomes  so  if 
we  take  the  masses  at  work  into  account. 

From  these  three  "laws,"  Newton  showed  that 
the  force  governing  the  motions  of  the  planets 
was  in  each  case  directed  to  the  Sun,  and  was  as 
the  inverse  square  of  the  distance  from  him.  Re- 
versely he  showed  that  such  being  the  law  of 
gravitation,  the  orbits  must  all  be  conic  sections. 
Ellipses  and  But  conic  sections  are  of  two  kinds,  —  ellipses 
or  closed  curves,  and  hyperbolas  or  curves  that  do 
not  return  into  themselves.  Clearly  permanent 
members  of  a  system  must  travel  in  the  first  of 
these  two  classes  of  curves,  visitors  only  in  the 
second.  Here,  then,  we  have  an  instant  criterion 
for  distinguishing  bodies  that  belong  to  our  system 
from  those  that  visit  it  from  without. 


Our  Solar  System 


Which  of  the  two  orbits  a  body  is  pursuing  may 
be  determined  either  by  actually  finding  the  body's 
path  or  by  finding  the  distance  of  the  body  from 
the  Sun  and  its  speed  at  the  moment.  For  an 
interesting  equation  connects  the  speed  with  the 
distance,  giving  the  major  axis  of  the  orbit,  upon 
which  alone  the  class  of  curve  depends.  This 
equation  is 


in  which  the  —  sign  betokens  the  ellipse,  the  -}-  sign  the 
hyperbola. 

Suppose  a  body  at  p  moving  along  the  curve  whose  tan- 
gent is  pt  with  acceleration  f  always  directed  to  s.  Then 
z/,  the  resolved  part  of  the  acceleration  along  the  tangent, 
is  f  cos  ^. 


8  The  Solar  System 

The  resolved  part  of  the  velocity  v  along  sp  is  r, 
and  r  =  i>  cos  «/>  ; 

whence 


£  can  be  determined  from  the  actual  velocity  at  some 
point  in  the  orbit  (at  the  end  of  the  minor  axis,  for  instance, 
in  the  ellipse),  and  from  this  we  can  find  that 


where  a  is  the  semi-major  axis  of  the  curve,  the  upper  sign 
referring  to  the  ellipse,  the  lower  to  the  hyperbola. 

The  velocity  in  the  hyperbola  thus  exceeds  that 
in  the  ellipse,  and  the  dividing  line  between  the 
two  classes  of  curves  is  clearly  when  the  second 
term  is  zero. 

Consequently 

7/2=^ 

r 

is  the  velocity  which  at  any  given  distance  r  sepa- 
rates the  bodies  moving  in  ellipses  from  those 
moving  in  hyperbolas,  the  sheep  from  the  goats. 

ffeA 

r 

is  called  the  parabolic  velocity,  but  the  student 
should  be  careful  to  remember  that  the  parabola 
is  a  mathematical  conception,  not  a  physical  fact. 


Our  Solar  System 


It  is  a  conceptual  dividing  line  between  ellipses 
and  hyperbolas,  the  paling  between  the  sheep  and 
the  goats. 

Now  the  planets  all  move  in  ellipses.  They 
are  therefore  under  the  Sun's  control  and  form 
part  of  his  system. 

Occasionally  stones  fall  out  of  the  sky  on  to  Meteors. 
the  earth.  Suddenly  a  flash  occurs  overhead,  a 
detonation  follows,  and  then  if  the  observer  be 
near  enough,  a  mass  of  stone  or  iron  is  seen  to 
bury  itself  in  the  ground.  This  is  a  meteorite, 
aerolite,  or  bolide,  a  far  wanderer  come  at  last 
to  rest. 

The  flash,  the  report,  and  the  fused  exterior  of 
the  mass  found  are  due  to  the  meteor's  striking 
against  our  air.  The  bodies  enter  the  upper  at- 
mosphere at  speeds  of  from  ten  to  forty  miles  a 
second,  and  such  speeds  are  equivalent  to  immers- 
ing them  in  a  blow-pipe  flame  of  a  temperature 
of  many  thousands  of  degrees.  For  the  tempera- 
ture of  a  gas  is  as  the  mean  velocity-square  of  its 
molecules,  and  the  rush  of  the  meteor  produces 
the  same  effect  as  if  the  molecules  of  the  air  were 
moving  and  the  air  therefore  very  hot. 

Its  outward  condition  is  a  consequence  of  the  Previously 
last  stage  in  its  journey,  but  its  inner  state  at  c< 
times  continues  to  bear  witness  to  a  previous  con- 


io  The  Solar  System 

dition.  If  the  mass  be  large,  time  does  not  suffice 
to  fuse  more  than  its  exterior,  and  the  interior  re- 
tains the  cold  of  interplanetary  space.  As  Young 
tells  us,  one  of  the  fragments  of  the  Dhurmsala 
meteorite  in  India  was  found  in  moist  earth,  half 
an  hour  or  so  after  its  fall,  coated  with  ice  ! 

Their  orbits  But  their  speed  is  the  real  tell-tale  upon  their 
ellipses.  past  An  jngenjous  investigation  by  the  late  Pro- 
fessor Newton,  whose  specialty  was  these  very 
things,  proved  that  ninety  per  cent.,  and  probably 
all  of  the  meteorites  for  which  we  have  sufficient 
data,  were  traveling,  before  their  encounter  with 
the  earth,  in  orbits  not  parabolic,  but  elliptic,  like 
those  of  the  short-period  comets,  and  were  moving 
direct.  They  come  to  us,  therefore,  not  from  the 
stars,  but  from  the  Sun's  own  domain.  They, 
too,  then  are  members  of  the  system. 

Their  origin.  Most  interesting  is  their  constitution  in  its  bear- 
ing upon  their  origin.  Some  are  stone,  some  iron  — - 
meteoric  iron  joined  with  nickel.  Now  the  iron 
meteorites  are  saturated  with  occluded  gases, 
which  can  be  extracted  from  them  by  suitable 
processes,  and  which  cannot  have  been  occluded 
originally  except  in  the  molten  interior  of  a  sun, 
intense  heat  and  excessive  pressure  being  neces- 
sary ;  and  as  they  are  now  ungathered  in  remnants 
of  our  own  once  nebulous  mass,  they  must  betray 


Our  Solar  System  1 1 

what  that  nebulous  mass  was  to  begin  with ;  for 
in  their  subsequent  history  there  has  been  no- 
thing to  make  them  what  they  are.  They  cannot 
have  come  from  our  present  sun,  since  it  became  a 
sun,  as  their  orbits  conclusively  show.  They  must 
have  come  from  the  sun  our  system  had  before 
the  catastrophe,  which  caused  the  nebula  which 
caused  our  Sun,  occurred.  They  antedate  the 
creation  of  the  nebula  itself  which  our  nebular 
hypothesis  posits  as  the  beginning  of  things. 
They  are  old  with  an  age  which  staggers  imagina- 
tion ;  older  in  cycles  of  evolution,  if  not  in  years, 
than  anything  we  see  in  the  countless  spangles 
of  a  winter's  night  in  the  blue-black  firmament  of 
sky.  Before  the  silent  tale  they  tell,  history 
shrinks  into  yesterday,  the  Earth's  career  into 
the  day  before,  and  the  evolving  of  the  solar  sys- 
tem itself  into  modernity.  Through  that  strange 
Widmannstattian  fretwork  that  marks  their  sur- 
face like  the  lacing  of  frost-work  on  a  window- 
pane,  we  seem  to  be  gazing  past  the  iron  bars  into 
the  immensity,  not  of  space  alone,  but  of  eternity. 

Next  to  meteors,  and  doubtless  close  to  them  Shooting- 
in  kind,  come  shooting-stars.     Superficial  distinc- 
tions have  caused  them  to  be  classed  apart,  but  in 
all  likelihood  size  alone  separates  the  two. 

In  the  case  of  shooting-stars,  we  have  the  flash, 


12  The  Solar  System 

the  lingering  scarf  of  light  left  when  the  body  it- 
self has  eluded  us,  but  no  sound  is  heard,  and 
nothing  reaches  the  earth. 

Meteor-  The  visitants  come,  too,  in  swarms.     They  have 

their  times  and  seasons.  Different  nights  of  the 
year  are  consecrate  to  special  flights ;  and  the  suc- 
cessive years  bring  back  the  same  flights  like 
birds  that  honk  overhead  at  the  same  recurrent 
season  of  the  year. 

Such  regularity  has  caused  them  to  be  noted 
and  studied,  and  we  have  now  a  score  of  well- 
recognized  congeries  of  shooting-stars  or  meteoric 
streams,  known,  for  example,  as  the  Leonids,  the 
Perseids,  the  Andromedes.  Each  swarm  has  its 
radiant  or  perspective  point  from  which  all  its 
members  seem  to  come.  From  this  radiant  it 
derives  its  name,  the  Leonids  seeming  to  come 
from  a  point  in  the  constellation  Leo,  the  Orionids 
from  the  constellation  of  Orion,  and  the  Lyrids 
from  the  Lyre. 

Their  speeds.  Each  of  these  swarms  enters  our  atmosphere 
with  cosmic  speed,  all  the  shooting-stars  of  one 
swarm  traveling  at  the  same  rate  ;  but  each  swarm 
has  its  own  distinctive  velocity.  The  Andromedes 
move  relatively  slowly,  —  eleven  miles  a  second,  — 
and  are  reddish.  They  overtake  us  ;  this  accounts 
for  their  sluggishness,  and  their  sluggishness  ex- 


Our  Solar  System  1 3 

plains  their  color.  They  are  only  red-hot.  The 
Perseids  move  with  medium  velocity.  They  strike 
us  on  the  quarter  at  twenty-five  miles  a  second, 
and  they  are  yellow.  The  Leonids,  or  November 
meteors  par  excellence,  meet  us  head  on  at  forty- 
three  miles  an  Hour, "their  swiftness  giving  them  a 
bluish-green  tint  or  a  white  heat. 

To  Professor  Newton  again  we  owe  our  first  Their  orbits 
step  to  knowledge  of  them.  After  the  shower  of 
the  Leonids  in  1866,  he  determined,  from  all  the 
observations  upon  them,  five  orbits  which  they 
might  have  pursued;  and  then  Adams,  of  Nep- 
tunian fame,  from  the  motion  of  their  node,  showed 
that  only  one  of  the  five,  an  orbit  with  a  period 
of  thirty-three  years,  would  satisfy  the  problem. 
Thus  was  explained  the  similar  shower  of  1833 
and  the  yet  earlier  one  of  1799,  seen  by  Hum- 
boldt.  We  should  have  had  them  again  in  1900, 
but  that  Jupiter  probably  interfered. 

In  the  same  way,  the  Andromedes  prove  to 
travel  in  an  orbit  whose  period  is  thirteen  years, 
and  whose  aphelion  lies  just  outside  the  orbit  of 
Jupiter.  So,  also,  the  Perseids  pursue  a  closed 
orbit,  but  a  much  larger  one,  which  takes  them 
far  beyond  the  orbit  of  Neptune. 

Shortly  after  Newton  and  Adams  had  worked 
out  the  path  of  the  November  meteors,  Schiapa- 


The  Solar  System 


Association     relli  attacked  the  orbit  of  the  Perseids,  or  August 

of  meteor-  .. 

streams  with    meteors,  and  to  the  astonishment  of  the  scientific 
world  brought  -out  the  surprising  fact  that  they 


I  Andro'medes  and  Biela's  Comet -1772. 
D  Leonids  and  Tempel's  Comet- 1 8 66-1 
(Retrograding  Comet  of  shortest  period). 


m  Perseids  and  Tunic's  Comet  -  1862-m. 
IV  Lyrids  and  Comet-  I86I-I. 


FIG.  III.     METEOR  STREAMS. 


traveled  in  an  orbit  substantially  coincident  with 
that  of  the  great  comet  of  1862,  known  as  Tuttle's 
comet  (1862  III.).  About  the  same  time,  Leverrier 
published  his  orbit  of  the  Leonids,  and  nearly 


Our  Solar  System  1 5 

simultaneously  Oppolzer,  the  great  comet  com- 
puter, published  his  of  Tern  pel's  comet  of  1866 
(1866  I.),  and  the  two  were  found  to  be  practically 
identical.  Here  were  two  identities  which  could 
hardly  be  the  result  of  chance.  Researches  since 
have  added  to  the  number  of  such  comet-meteor 
associations.  Professor  Herschel  catalogues 
seventy-six ;  and  four  pairs  —  the  Leonids  and 
Tempel's  comet,  the  Perseids  and  Tuttle's  comet, 
the  Andromedes  and  Biela's  comet,  and  the  Lyrids 
and  the  comet  of  1861  (1861  I.)  — are  shown  in 
the  diagram  on  the  opposite  page. 

Thus  are  comets  and  meteors  connected.     But  Comets 

.  ....     become 

we  know  more  about  their  connection  than  this  meteor- 
simple   fact  of  association.     We  know  that   the  sl 
one  becomes  the  other,  for  we  have  seen  the  pro- 
cess of  transformation  take  place  practically  under 
our  very  eyes.     Biela's  comet  was  for  many  re- 
turns a  well-ordered  member  of  Jupiter's  comet- 
family,  of  which  family  we  shall  have  more  to  say 
in  the  fifth  chapter.     Up  to  1839  ft  na^  returned 
with   due   regularity    and   without    incident.     In 
1846,  it  again  appeared  on  time,  but  thereupon 
proceeded  to  do  something  very  strange  and  then 
unheard-of.     In  mid-career  it  split.     It  was  first  . 
seen  on  November  28,  and  presented  the  appear- 
ance of  the  usual  comet.     By  December  19  it  had 


1 6  The  Solar  System 

become  pear-shaped,  and  on  January  13  it  divided, 
the  two  halves  at  first  separating,  and  thenceforth 
traveling  side  by  side  at  a  distance  of  one  hundred 
and  sixty  thousand  miles  for  the  subsequent  four 
months  during  which  they  continued  visible.  A 
bridge  of  light  sometimes  spanned  the  interval 
between  them. 

In  1852  the  two  returned.  The  distance  be- 
tween the  pair  had  now  increased  to  one  million 
five  hundred  thousand  miles,  and  they  traveled 
thus  during  the  time  of  their  visibility. 

Neither  has  ever  been  seen  since;  but  in  1872, 
just  when  the  Earth  was  passing  the  track  of  the 
lost  heavenly  twins,  on  November  27,  occurred  a 
brilliant  star-shower.  The  German  astronomer, 
Klinkerfues,  was  so  impressed  with  the  belief 
that  this  must  be  the  remains  of  the  comet,  and 
that  the  comet  itself,  or  what  was  left  of  it,  would 
be  seen  exactly  opposite  the  radiant,  that  he  tele- 
graphed at  once  to  Pogson,  the  government  as- 
tronomer at  Madras,  India  :  "  Biela  touched  Earth 
November  27 ;  search  near  Theta  Centauri."  Pog- 
son looked.  Clouds  at  first  prevented,  but  on 
the  third  morning  it  was  fair,  and  he  saw  in  the 
predicted  place  a  comet  with  a  round  head  and  a 
faint  tail  moving  as  it  should  have  done.  The 
next  morning  he  observed  it  still  better,  and  in  its 


Our  Solar  System  1 7 

proper  place.  Oppolzer,  by  assuming  the  major 
axis,  showed  that  this  may  have  been  Biela's  comet. 

Since  then,  other  comets  have  been  observed  to 
split  up,  due  to  the  action  of  the  planets  near 
which  they  chance  to  pass ;  and  Callandreau  has 
shown  that  the  event  ought  not  to  be  so  very 
uncommon. 

Another   point   connected   with   these   meteor  Meteor 

,        ,-,      ,       r     ,  .  streams 

streams  must  be  noticed.     Each  of  them  is  asso-  attendant 
ciated  with  the  orbit  of  some  particular  planet.  upon  Planets- 
The  planet  in  some  sense  shares  with  the  Sun  a 
control   over  the   stream.*    It  cannot  cause   the 
stream  to  circle  round  itself,  but  it  can,  and  does, 
cause  it  to  pay  periodic  obeisance  to  its  might. 
The  stream's  perihelion  remains  at  the  Sun,  but 
its  aphelion  becomes  its  periplaneta.     It  sweeps 
about  the  planet  at  the  one  end  of  its  path  some- 
what as  it  sweeps  round  the  Sun  at  the  other. 

The  Andromedes  are  thus  dependent  on  Jupi- 
ter, the  Leonids  on  Uranus  ;  while  the  Perseids 
and  the  Lyrids  go  out  to  meet  the  unknown  planet 
which  circles  at  a  distance  of  about  forty-five  as- 
tronomical units  from  the  Sun. 

It  may  seem  to  you  strange  to  speak  thus  con- 
fidently of  what  no  mortal  eye  has  seen,  but  the 
finger  of  the  sign-board  of  phenomena  points  so 
clearly  as  to  justify  the  definite  article.  The  eye 
of  analysis  has  already  suspected  the  invisible. 


i8 


The  Solar  System 


Conspicuous 
comets. 


Parabolic 
comets. 


In  our  identification  of  the  members  of  our  sys- 
tem we  have  thus  got  steadily  farther  and  farther 
away.  We  began  with  the  planets.  Then  we 
attacked  the  less  evident  and  more  erratic  bodies, 
and  we  found  that  the  nearest  of  them,  the  mete- 
orites, were  after  all  fellow-members,  and  circled 
quite  near  us,  their  orbits  being  comparable  with, 
and  possibly  not  alien  to,  the  short-period  comets. 

Next  we  found  the  shooting-stars,  the  meteor 
streams,  to  be  sun-controlled  but  traveling  farther 
yet  out  into  space,  and  connected  with  comets 
known  to  be  periodic.  We  have  now  to  take  an- 
other step  outward  to  the  comets  non-periodic, 
among  which  the  most  conspicuous  of  those  visit- 
ants are  numbered. 

Non-periodic  we  may  call  them  pending  investi- 
gation. For  their  orbits  are  so  vast  that  we  know 
but  vaguely  what  their  major  axes  are. 

Some  four  hundred  of  these  stars  with  tresses 
have  been  seen  from  the  earliest  times  of  which 
we  have  records  to  the  present  day.  Not  a  year 
passes  that  several  are  not  discovered,  but  conspic- 
uous ones  are  not  over-common.  In  the  last 
forty  years  there  has  been  but  one  of  superlative 
mien,  and  that  was  twenty  years  ago.  The  pre- 
sent generation  has  no  conception  of  what  a  comet 
worthy  the  name  can  be.  One  of  my  first  recollec- 


Our  Solar  System 


FIG.  IV.    CONSPICUOUS  COMETS. 


2O  The  Solar  System 

tions,  if  not  my  very  first,  is  of  such  an  one,  and 
the  memory  of  it  has  never  been  approached  by  any 
celestial  phenomenon  since.  A  total  eclipse  of  the 
Sun  is  commonplace  beside  it.  Of  the  four  hun- 
dred up  to  now  observed,  the  greater  part  move 
in  orbits  differing  so  little  from  the  parabolic  for 
the  small  fraction  of  their  paths  we  are  privileged 
to  mark  that  to  all  intent  they  travel  in  parabolas. 
They  lean,  however,  to  the  side  of  the  ellipse. 
Most  of  them  frankly  do  so,  although  so  slightly 
that  to  determine  their  major  axes  to  any  degree 
of  accuracy  is  not  possible.  Very  few,  three  or 
four  perhaps,  hint  at  hyperbolas.  Not  one  is  such 
beyond  question,  however  slightly.  In  my  notes 
on  Galle's  catalogue,  I  find  the  following  gloss  at 
the  end  of  the  list :  "  There  is  not  a  single  undis- 
puted hyperbolic  orbit ;  nor  is  there  one  in  which 
the  computed  non-hyperbolic  orbits  are  not  in  the 
majority." 

Their  orbits.  From  this  fact  of  a  practical  parabolicity  of 
path  many  astronomers  have  argued  the  exterri- 
toriality of  these  bodies,  and  early  in  the  last  cen- 
tury Laplace  set  himself  the  problem  of  finding 
the  probability  of  hyperbolic  to  elliptic  orbits  on 
the  theory  that  they  all  came  to  the  Sun  from 
stellar  space.  In  spite  of  several  mistakes  in  his 
work,  first  pointed  out  by  Gauss,  he  reached  a 


Our  Solar  System 


21 


conclusion  which  is  correct  in  quality  :  that  the 
number  of  hyperbolic  orbits  to  elliptic  should  be 
very  small,  less  than  one  in  the  whole  number 
already  seen,  on  the  tacit  assumption  that  the  Sun 
was  at  rest. 

But  the  Sun  is  not  at  rest.     It  is  traveling  at    Conclusion  as 
the  rate  of  eleven  miles  a  second  towards  a  point    with° 
in  the  constellation  Hercules,  carrying  its  retinue    system- 
with  it ;  and  this  motion  quite  alters  the  result. 
Instead  of  a  great  preponderance  of  elliptic  orbits, 
the  solution  shows  in  this  case  a  large  excess  of 
hyperbolic  ones.     And  in  most  of  the  orbits  the 
hyperbolicity   would   be   marked,   not    faint   and 
doubtful.     To  Schiaparelli  we  owe  the  first  sug- 
gestion of  this  fact,  and,  in  1895,  to  Fabry,  of  the 
observatory  of  Marseilles,  a  very  elegant  and  con- 
clusive memoir  on  the  subject.1 

In  view  of  this  we  see  that  comets  behave  not 
as  they  would,  did  they  come  to  us  as  visitors  from 
other  stars,  but  just  as  they  should,  considered 
as  distant  members  of  our  own  system.  Comets, 
then,  are  also  all  co-members  of  the  system. 

That  there  is  quite  room  enough  within  the   The  sun's 
Sun's  paramount  domain  for  their  gigantic  orbits 
becomes  evident  when  we  consider  the  distance 
to  which  that  domain   extends.     Measured  even 

1  Annales  de  la  Faculte  des  Sciences  de  Marseille, 


22  The  Solar  System 

on  the  vast  scale  of  our  solar  system,  the  gap 
which  sunders  it  from  the  nearest  fixed  star  is 
something  enormous.  Two  hundred  and  seventy- 
five  thousand  times  our  distance  from  the  sun  is 
the  space  that  divides  us  from  the  next  sun,  the 
star  a  Centauri.  This  distance  is  found  by  not- 
ing the  shift  in  the  star's  position  due  to  the  ex- 
treme swing  of  the  Earth  in  her  orbit  called  the 
annual  parallax.  It  is  a  very  minute  displacement 
at  most,  and  requires  perhaps  the  most  delicate  of 
all  astronomical  refinement  to  detect.  Inciden- 
tally it  affords  conclusive  evidence  of  itself  that 
the  Earth  goes  round  the  Sun,  not  the  Sun  round 
the  Earth. 

a  Centauri.  Fortunately  a  Centauri,  our  nearest  stellar 
neighbor,  is  a  double  star,  a  binary  system,  and 
thus  of  itself  affords  us  information  of  the  region 
over  which  it  exercises  control.  Assuming  that 
gravity  acts  there  just  as  it  does  here,  — any  other 
possible  assumption  implies  that  the  force  de- 
pends on  the  orientation,  which  does  not  seem 
rational,1  —  we  can  deduce  from  the  motion  of  the 

1  Binaries  move  in  apparent  ellipses.  Parallel  projection  keeps 
an  ellipse  an  ellipse  and  the  centre  the  centre.  From  the  general 
polar  equation  of  a  conic  and  the  differential  equation  of  the  orbit, 

/=»*("+£)• 

it  appears  that  the  only  laws  of  force  which  do  not  depend  on 


Our  Solar  System  23 

pair  their  united  mass.  It  comes  out  twice  that  of 
our  Sun.  Now,  as  gravity  is  as  ^-,  we  have,  call- 

ing the  whole  distance  from  us  to  them  a,  the 
following  quadratic  to  give  us  d,  the  boundary  dis- 
tance between  the  two  domains,  our  Sun's  and 
a  Centauri's, 

m          m 


from  which  we  find  the  dividing  line  between  the 
Sun's  domain  and  a  Centauri's  to  be  114,000 
astronomical  units. 

Neptune,  the  farthest  known  planet  at  present, 
is  but  thirty  astronomical  units  away,  or  about 
loVo  om*y  °f  tne  distance  to  the  limit  of  the  Sun's 
domain.  How  nestled  we  all  are  under  the  Sun's 
protecting  wing  is  evident.  It  is  no  wonder  that 
the  remotest  comets  seem  almost  infinitely  distant 
at  their  aphelion,  though  part  and  parcel  of  the 
brood. 

Coming  back  now  from  these  chill  outer  con-  The  several 
fines  of  the  Sun's  territory  to  the  inner  family  F 
circle  gathered  about  the  hearth  or  focus  of  all 
these  ellipses,  occupied  by  the  Sun,  —  for  such  is 

9,  that  is,  on  the  orientation,  are/=  cr,  which  is  negatived  by 
the  fact  that  no  star  has  yet  been  found  in  the  centre  of  the 
apparent  ellipse,  and/=  -^.,  which  is  thus  the  only  law  possible 
which  is  rational.  It  is  thus  ably  put  by  Moulton  (Celestial 
Mechanics,  1902). 


! 


24  The  Solar  System 

the  literal  meaning  of  the  word  "  focus,"  —  we 
must  note  how  the  main  bodies  and  yet  smaller 
particles  are  severally  ranged  about  it. 

Terrestrial  Humboldt  divided  the  planets  into  two  groups  : 
P?adn^ts.J°r  the  terrestrial  planets  and  the  major  planets,  and 
this  classification  one  shall  still  find  in  many  a 
text-book.  But  it  has  long  since  ceased  to  con- 
tain even  a  specious  distinction.  The  so-called 
terrestrial  planets  differ  among  themselves  quite 
as  much  as  any  of  them  do  from  the  major  planets. 
From  our  present  knowledge  it  would  be  much 
nearer  the  mark  to  divide  the  eight  into  pairs, 
Mercury  and  Venus,  the  Earth  and  Mars,  Jupiter 
and  Saturn,  Uranus  and  Neptune  ;  yet  even  be- 
tween the  members  of  each  pair  are  notable  dif- 
ferences, to  say  nothing  of  the  asteroids  which 
throng  the  space  betwixt  Jupiter  and  Mars. 

Of  the  differences,  it  will  be  the  province  of  the 

succeeding  chapters  to  speak ;  but  before  doing 

so,  let  us  take  a  bird's-eye  view  of  the  whole.  ' 

Solar  System     Our  own  Solar  System  has  one  characteristic, 

one"8        r  a  general  family  trait,  which  distinguishes  it  from 

many  that  lie  round  about  it  in  space  ;  for  we  may 

not  doubt  that  the  stars  are  centres  to  systems  of 

their  own.     We  have  not  only  analogy  to  guide 

us  to  this  deduction,  but  we  already  have  glints  of 

evidence  of  the  fact.     Our  system  differs,  how- 


Our  Solar  System  25 

ever,  from  many  of  its  neighbors  in  being  a  single- 
sun  system.  This  is  a  very  important  and  funda- 
mental distinction.  To  begin  with,  it  makes 
cosmic  principles  much  easier  to  understand.  We 
think  celestial  mechanics  abstruse  enough  as  they 
are,  but  ours  are  child's  play  to  the  complications 
which  two  suns,  to  say  naught  of  three  or  four, 
would  introduce  into  any  system  over  which  they 
jointly  held  sway.  It  is  problems  of  this  nature 
which  Professor  Darwin  and  other  modern  analysts 
are  trying  to  unravel.  Difficult  as  the  concep- 
tions are,  it  is  a  question  whether  life  itself  would 
not  be  quite  as  difficult,  under  such  conditions. 
Take  our  nearest  stellar  neighbor,  a  Centauri,  for 
instance,  and  consider  what  a  planet  circling  round 
either  or  both  of  its  suns  would  be  called  upon  to 
undergo.  Certainly  our  orderly  succession  of 
phenomena  would  be  seriously  disturbed  to  the 
consequent  inconsequency  of  development  upon 
its  surface.  Day  and  night  would  become  mean- 
ingless terms,  and  organisms  would  have  to  put  up 
with  variations  which  make  imagination  stare. 

For  fashioning  worlds    like   the   terrestrial,    a 
single-star  system  is,  in  general,  a  prerequisite. 

This  oneness  is   due  to  the  system's  original    Due  to 
small  moment  of  momentum.     A  minimum  mo-   ^ 
ment  of  momentum  is  caused  by  the  centralization    momentum 


26  The  Solar.  System 

of  the  mass  ;  a  maximum  by  its  equal  division  into 
two  or  more.  If  we  calculate  the  moment  of  mo- 
mentum of  the  Solar  System  to-day,  and  compare 
it  with  that  of  any  binary  system,  we  shall  find  it 
in  comparison  almost  vanishingly  small. 

The  system,  61  Cygni,  with  only  one  fifth  of  its 
mass,  has  a  moment  of  momentum  two  hundred 
and  fifty  times  as  great,  and  that  of  a  Centauri, 
which  has  twice  the  mass,  has  two  thousand  times 
the  moment. 

This  means  that  in  the  region  of  space,  which 
made  room  to  the  solar  nebula,  the  individual  mo- 
tions must  have  been  either  small  or  equally  large 
in  all  directions,  the  negative  motions  almost 
exactly  canceling  out  with  the  positive  ones. 


II 

MERCURY 

NEAREST  to  the  Sun  of  all  the  bodies  of  the 
system,  excepting  only  the  swarm  of  particles 
which  give  us  the  Zodiacal  Light,  is  Mercury. 

Till  very  lately,  we  knew  next  to  nothing  about  Till  lately 

.  .         ,  11.        very  little 

this  planet.       Its  doings,  as  represented  by  its  known  of  it. 

path,  were  well  determined,  but  its  self  not  at  all. 

Part  cause  of  this  was  its  nearness  to  the  Sun ;  a 

part,  its  being  an  inferior  planet,  and  thus  being 

but  ill  seen  when  most  observable ;  for  when  at 

its  greatest  apparent  distance  from  the  Sun,  — 

at  one  of  its  elongations,  as  it  is  called,  —  half  of 

it  alone  is  illuminated,  and  that  half  but  poorly. 

Secondly,  when  it  appears  to  the  naked  eye,  and 

when  in  consequence  it  is  generally  looked  for 

with  the  telescope,  it  is  deep  sunk  in  the  vapors 

of  the  horizon,  and  the  air  through  which  it  is 

seen  is  so  tremulous  that  its  disk,  in  consequence, 

is  ill-defined.     As  this  was  supposed  the  best  time 

for  observation,  the  disk  was  deemed  inscrutable. 

But  the  obvious  is  to  be  avoided.     Acting  upon  Markings 

..,«,.  ,,.     .         nn  detected  in 

this  principle,   Schiaparelli,  in  1889,  took  a  new  1889. 
departure  by  systematically  observing  Mercury  by 


28  The  Solar  System 

day.  He  was  before  long  rewarded.  Markings 
began  to  show  themselves  upon  the  little  disk, 
difficult  of  detection,  indeed,  but  still  visible 
enough  to  enable  him  to  be  satisfied  of  their  per- 
manency ;  and  then  the  markings  disclosed  of 
themselves  a  very  singular  fact.  From  the  sta- 
bility of  their  positions,  it  became  evident  that 
the  planet  rotated  upon  its  axis  in  the  same  time 
that  it  revolved  about  the  sun. 

Rotation  and  Let  us  consider  a  moment  how  it  was  the  mark- 
iTodlronous.  mgs  disclosed  this  fact.  Suppose,  for  simplicity, 
a  body  revolving  round  its  primary  in  a  circle  and 
made  visible  by  the  light  received  from  it.  Fur- 
thermore, suppose  the  revolving  body  to  have 
markings  upon  it,  and  to  rotate  once  upon  its  axis 
as  it  makes  one  revolution  round  its  sun.  Clearly 
it  will  always  present  the  same  face  to  the  central 
attracting  and  illuminating  body,  and  therefore 
the  markings  will  maintain  an  invariable  position 
with  regard  to  the  illuminated  face.  To  an  out- 
sider, the  planet,  if  inferior,  will  present  the  phases 
of  the  Moon.  Unlike  the  Moon,  however,  the 
illumination  will  not  sweep  over  an  invariable  face, 
but  lighting  and  lighted  will  rotate  together ;  for 
in  the  case  of  the  Moon,  we  are  the  attracting,  but 
not  the  illuminating,  body  ;  in  the  case  of  a  planet, 
the  Sun  is  both. 


Mercury  29 


Schiaparelli  was  the  only  one  to  see  these  mark-  Flagstaff 

.  corroborates 

ings  till  1896,  when  the  subject  was  taken  up  at  Schiaparelli. 
Flagstaff.  The  planet  was  at  the  time  coming 
out  from  inferior  conjunction,  and  was  at  first  no 
easy  matter  to  find  ;  for  in  relative  visibility  Mer- 
cury behaves  like  the  Moon.  Size  of  disk  does 
not  begin  to  compensate  for  phase,  as  calculation 
would  lead  one  to  expect ;  because  obliquity  of 
illumination  greatly  enfeebles  its  amount.  The 
planet  presented  so  faint  a  contrast  with  the  sky 
that  on  one  occasion  an  assistant,  coming  to  look 
at  it  through  the  telescope,  could  not  see  it  until 
its  exact  position  was  pointed  out  to  him  ;  and  I 
always  picked  it  up  myself  by  trailing  it  across 
the  field,  an  object  in  motion  being  much  more 
evident  than  one  at  rest,  as  every  hunter  knows. 
Nor  could  I  at  first  make  much  out  of  it ;  it  was 
only  a  pretty  little  moon  nearly  lost  in  the  vast 
blue  sky.  To  my  surprise,  however,  as  it  left 
elongation  to  return  to  the  Sun,  it  grew  brighter 
and  brighter,  and  distinct  dark  markings  came  out 
upon  its  disk.  The  best  views  occurred  when 
popular  almanacs  inform  their  readers  :  "  Mercury 
invisible  during  the  month."  In  the  clear. sky 
and  steady  air  of  Arizona  and  Mexico  the  mark- 
ings were  not  especially  difficult  objects,  though 
more  difficult  than  the  canals  on  Mars.  They 


30  The  Solar  System 

were  narrow,  irregular  lines  and  very  dark.  They 
were  not  in  the  least  like  the  markings  on  Mars. 
There  were  no  large  patches  of  shade  on  the  one 
hand,  nor  fine,  regular  pencilings  on  the  other. 
Its  lines  were  fairly  straight,  but  broken  and  of 
varying  width.  "  Cracks  "  best  explains  their  ap- 
pearance, and  probably  their  nature. 

Their  positions  were  unmoved,  even  after  as 
much  as  five  hours'  interval. 


Nov.  1  — 21h  16m.  Nov.  2  —  Oh  38m-45m.  Nov.  2  —  2h  40m. 

FIG.  V. 

TRIAD  OF  DRAWINGS,  Nov.  1-2,  1896. 
No  shift  in  markings  during  sh  24m. 

Markings          As  I  continued  to  map  them,  I  marked  that 
iteration  in    while   their   relation   to   the  terminator  was  un- 
longitude.      cnange(j  ^y  the  hours,  it  was  slowly  shifting  with 
the  days.     The  lines  were  gradually  passing  over 
its  edge,  and  it  dawned  on  me  what  I  was  witness- 
ing :  the  swaying,  or  libration,  of  the  planet  in 
longitude  due  to  the  eccentricity  of  the  planet's 
orbit. 


Mercury 


o      'J 


Si 


3   I 

5  II 
2    3 


5    3 


•<  r- 


IG 
R 


32  The  Solar  System 

Cause  of          Libration   in    longitude  is  a   necessary   conse- 

libration  in  r   ,  ,  -,      .  ,  ,  •  r        -, 

longitude,  quence  of  the  planet  s  moving  in  a  focal  conic. 
The  moment  of  rotation  of  a  body  of  Mercury's 
mass  is  so  great  that  it  would  take  more  than  the 
Sun's  might  to  suddenly  alter  it.  The  planet 
turns  upon  its  axis,  therefore,  with  a  uniform  spin. 
But  its  angular  speed  in  its  orbit  is  not  uniform. 
Since  the  radius  vector  sweeps  out  equal  areas  in 
equal  times,  the  angular  velocity  near  perihelion 
exceeds  that  near  aphelion.  The  revolution  gains 
on  the  rotation  here,  and  at  the  end  of  a  certain 
time  reaches  its  maximum  ;  after  which  the  rota- 
tion gains  on  the  revolution,  and  the  deficiency  is 
made  up  again  at  aphelion. 

Maximum         To   determine   what   the  maximum  is,  and  where,  we 

Hbration  in    ^ave  :  tnat  t^ie  mean  angular  velocity  of  revolution  in  the 

longitude,      ellipse  is  the  angular  velocity  of  a  body  supposed  to  be 

describing  a  circle  in  the  time  occupied  by  the  planet  in 

the  ellipse.     The  area  of  the  ellipse  being  irab,  and  the 

period  J1,  the  areal  velocity  in  the  ellipse,  which  is  con- 

stant, is 


T  ' 

This  is  the  areal  velocity  in  a  circle  of  radius  *J  a  b  sup- 
posed described  in  the  same  time. 

To  find,  therefore,  the  point  on  the  ellipse  where  the 
radius  has  the  value  corresponding  to  the  mean  angular 
velocity,  we  must  take  the  expression  for  r  of  the  ellipse 
referred  to  its  focus  as  a  pole, 


Mercury  33 


--£  COS  V 

and  equate  it  to  that  of  the   circle   supposed  described 
about  that  focus  with  the  length  of  radius  */ab.      This 
geometrically  is  the  point  of  intersection  of  the  two  curves, 
since  the  value  of  r  is  common  to  both. 
Consequently  for  the  point  sought 


whence,  since 


and 

e 

In  the  case  of  Mercury,  e  =  .205605  ;  v,  the  true  anomaly 
of  the  point  of  maximum  libration,  is  therefore  98°  55'.  13. 


But 


where  E  is  the  eccentric  anomaly  ;  and  E  —  e  sin  E  =  M, 
where  M  is  the  mean  anomaly  ;  whence  v  —  M  •=.  C,  which 
is  the  amount  of  the  maximum  libration,  is  23°  40'  38". 

The  gain  or  loss  of  the  rotation  over  the  revo- 
lution is  the  same  thing  as  the  equation  of  the 
centre. 

We  have,  then,  in  the  libration,  a  most  conclu- 
sive and  interesting  proof  of  the  isochronism  of 
rotation  and  revolution. 

The  next  point  to  consider  is  what  caused  this 


34  The  Solar  System 

New  branch  isochronism.  This  question  raises  a  wholly  new 
mechanics.  set  °f  problems  in  celestial  mechanics  from  those 
in  which  celestial  mechanicians  were  wont  to  en- 
gage. Until  recently,  mathematical  astronomy 
dealt  almost  entirely  with  solids,  —  entirely  so  out- 
side the  consideration  of  the  Earth.  But  no  solid 
is  absolutely  rigid,  and  the  action  of  one  body 
upon  another  must  cause  mutual  deformation  of 
figure  and  give  rise  to  tides  in  the  two  masses. 
Darwin  has  shown 1  that  this  tidal  action  is  an  im- 
portant cosmic  factor,  one  which  has  played  as 
constructive  a  part  in  the  evolution  of  things  as 
gravitation  itself. 

Not  only  were  the  planets  not  rigid  in  the  past ; 
they  are  not  rigid  to-day.  So  far  as  we  can  judge, 
all  the  planets  behave  as  plastic  bodies  at  the 
present  moment.  So  great  are  the  masses  that, 
even  in  the  case  of  the  denser  and  cooler  ones, 
deformation  of  figure  seems  to  be  what  fluidity 
and  rotary  conditions  would  require.  They  are, 
therefore,  fit  subjects  for  tidal  action. 
Tides—  Owing  to  the  great  importance  of  the  subject, 

how  caused. 

and  to  the  fact  that  the  explanation  given  of  it 
in  almost  all  the  text-books  is  erroneous,  I  shall 
present  it  to  you  with  some  pains,  the  more  so 
that  the  action  may,  I  think,  be  outlined  quite 

1  Pro.  Roy.  Soc.  1878-81. 


Mercury  35 


simply.  The  prestige  of  Sir  Isaac  Newton's  name 
is  responsible  for  the  inertia  which  still  carries 
the  usual  explanation  rolling  down  the  ages.  He 
attempted  to  explain  the  tides  statically,  and  the 
account  he  gave  has  been  blindly  copied  and  per- 
petuated. But  the  problem  is  not  a  static,  but  a 
kinematic  one ;  the  body  acted  on  is  in  motion  at 
the  time  of  the  action,  and  this  entirely  changes 
the  result.  Let  me  give  you  an  analogous  in- 
stance of  the  impossibility  of  treating  a  problem 
of  motion  as  if  it  were  one  of  rest.  The  preces- 
sion of  the  equinoxes  is  a  case  in  point,  and  may 
be  seen  in  a  gyroscope.  If  a  weight  be  hung  on 
the  axis  of  the  wheel  while  the  latter  is  at  rest,  the 
wheel  instantly  turns  into  the  horizontal  plane 
and  stays  there.  This  is  a  case  of  statics.  If 
now  the  wheel  be  set  in  motion,  however  slightly, 
the  wheel,  instead  of  lying  down  in  the  plane  of 
the  pull  once  and  for  all,  simply  rotates  in  space 
without  any  change  of  inclination  whatever.  This 
is  a  case  of  kinematics.  Kinematic  questions 
always  thus  differ  from  static  ones. 

Nor  can  the  motion  be  tacked  on  afterward,  as 
simultaneity  is  of  the  essence  of  the  problem.  If 
the  effect  of  the  Earth's  rotation  was  merely  to 
carry  forward  the  crest  of  the  tide  through  fric- 
tion, it  is  the  deep-water  tides,  —  those  in  water 


The  Solar  System 


Disturbing 
force. 


over  1 2|  miles  deep,  not  the  shallow,  —  that  would 
be  nearest  under  the  Moon. 

Consider  a  body  revolving  freely  around  an- 
other in  a  circle,  and  disturbed  in  this  motion  by 
a  third.  This  is  the  case  with  any  particle  of  the 
ocean  when  we  neglect  pressure  and  friction. 
Connect  the  three  bodies  by  lines,  and,  keeping 
their  directions,  increase  their  lengths  inversely 


C  Centre  of  the  Earth. 

PA  Particle  at  the  Surface. 

PERTURBATTVE  ACTION 
EXEMPLIFYING  THE  ORIGIN  OF  THE  TIDES. 

FIG.   VII. 


as  their  squares,  and  join  the  ends.     The  disturb- 
ing force  will  be  represented  by  the  connecting 
line,  on  the  principle  of  the  composition  of  forces. 
CM*  _PM 

PM*  ~  NM; 

whence  PN  represents  in  amount  and  direction 
the  disturbing  or  tide-raising  force. 


Mercury  37 


If  M  be  far  away  compared  with  CP, 
BN—2CB  =  2p,  say; 
for  since  P  M  =  BM  =  D 

and  CB=p, 


NM 
whence 
whence  BM—NM=BN  =  2p. 

The  tide-  raising  force  /Wmay  be  resolved  into 
a  normal  disturbing  force  PL  and  a  tangential 
disturbing  force  LN.  From  the  fact  that  BN  is 
always  twice  CB,  we  find  for  the  vanishing  points 
of  the  normal  force  a  and  b,  those  where  the  angle 
BCP  =  54°  44'.  .The  whole  disturbing  force  is 
there  tangential. 

Now  consider  the  action  of  the  two  compo- 
nents ;  first,  that  of  the  tangential  factor.  At  F, 
the  whole  force  is  normal  and  acting  inward. 
From  its  minimum  here  the  tangential  force  rises 
to  a  maximum  at  a,  where  it  comprises  the  whole 
force.  It  then  subsides  to  zero  at  A.  During  this 
quadrant  it  has  been  urging  the  particle  onward 
in  its  own  direction  of  movement  FA.  At  A,  it 
changes  sign  and  becomes  a  retarding  force,  which 
attains  its  maximum  at  b,  and  then  sinks  to  zero 
again  at  E. 

In  consequence,  the  velocity  of  the  particle  due 


38  The  Solar  System 

to  the  disturbing  force  is  a  maximum  at  A  —  be- 
cause the  force  has  been  adding  increments  to  it 
up  to  this  point  —  and  a  minimum  at  F  and  E. 
The  particle,  by  traveling  fast,  lessens  the  curva- 
ture of  its  path  about  C,  since  the  pull  from  C  has 
less  time  to  act ;  and  reversely  by  traveling  slowly 
it  increases  this  curvature.  In  consequence,  then, 
of  this  component,  the  path  is  flattened  at  A  and 
bulged  at  E. 

The  normal  component  acts  inward  at  Fand  is 
proportional  to  CP.  It  helps  the  central  force  at 
F,  and  curves  the  path  the  more.  At  a  it  van- 
ishes, and  is  then  reversed,  acting  outward  or 
against  the  gravity  of  C.  It  thus  lessens  the 
curvature  from  a-  to  b.  It  thus  conspires  com- 
pletely with  the  tangential  component ;  and  the 
two  together  squeeze  the  orbit  into  an  ellipse  with 
its  longer  diameter  at  right  angles  to  the  line 
joining  C  to  M. 
Tide  analo-  The  tidal  action  on  a  particle  of  the  ocean  is 

gous  to 

moon's  varia-  thus  precisely  the  same,  neglecting  pressure  and 
friction,  as  that  of  the  Sun  upon  the  Moon's  orbit. 
This  deformation  of  the  Moon's  orbit  was  de- 
tected, probably  by  Aboul  Wefa,  nine  centuries 
ago.  It  is  called  the  Moon's  variation.  Thus  the 
tidal  wave  and  the  variation  are  analogous  exhibi- 
tions of  the  same  force. 


Mercury  39 


Friction  now  comes  in  to  modify  the  result.    At  Effect  of 
F,  in  consequence  of  the   tide-raising  force,  the    l 
particle  is  traveling  less  rapidly  than  the  rest  of 
the  Earth.     Friction,  therefore,  urges  it  on  and 
increases  its  tangential  velocity  up  to  some  point 
P't  where  its  speed  becomes  equal  to  the  mean 
speed  of  the  earth.     After  this,  its  speed  being 
greater  than  the  Earth's,  friction  retards  it,  until 
it  again  becomes  the  mean  at  P.     Then  friction 
begins  again  to  accelerate  it. 

In  consequence,  the  particle  is  accelerated  from 
Q  to  P',  retarded  from  P1  to  P,  and  then  acceler- 
ated again.  From  A  on,  friction  thus  helps  the 
retarding  tangential  force,  and  the  Earth  causes 
the  particle  to  turn  the  corner  of  the  ellipse  at  E 
sooner  than  it  otherwise  would.  The  tangential 
force  thus  reaches  its  maximum  earlier,  and  the 
crest  of  the  tide  is  thus  shifted  from  E  backward 
to  some  point  P. 

On  the  Earth,  in  the  case  of  the  ocean,  we  are 
dealing  with  superficial  tides.  In  celestial  me- 
chanics, it  is  the  substantial  tides,  or  tides  of  the 
whole  body,  with  which  we  are  concerned.  The 
latter  are  immensely  the  more  potent.  As  the 
tidal  crest  lies  ahead  of  the  line  joining  the  two 
bodies,  the  Sun  or  the  Moon  is  constantly  trying 
to  pull  it  back  into  this  line,  while  the  Earth  is 


ing  force. 


40  The  Solar  System 

striving  by  friction  to  set  it  at  right  angles  to  the 
line.  The  bulge,  therefore,  acts  as  a  brake  upon 
the  Earth's  rotation,  and  must  continue  so  to  act 
until  the  Earth's  rotation  and  revolution  coincide. 
Tide-gen erat-  Now  let  us  determine  the  tide  -  generating 
force 1 :  — 

Let  M=  mass  of  the  Earth  ; 
m  =  mass  of  the  Moon  ; 
x,y,z  =  ihe  coordinates  of  the  Moon  re- 
ferred to  the  Earth's  centre  ; 
r=its  distance; 

g,rj,£  =  the  coordinates  of  the  particle  re- 
ferred to  the  Earth's  centre ; 
p  =  its  distance. 

Then  the  Earth  describes  an  ellipse  round  the 
centre  of  inertia  of  the  Earth  and  Moon,  and  its 

acceleration  is  n\  toward  this  centre. 

To  bring  it  to  rest,  we  must  apply  to  it  an  ac- 
celeration,   ^r>  of  which  the  accelerations  along 

the  coordinates  are,  — 

m    x  my  m     z 

"a'  r>  ~      rz'  r'     ~r*  '  r' 

Now  cos^  =  ^.l+->/.^  +  ^.-C 

r     p  ^  r     p^  r    p 

and  r  p  cos  z  =  x  |  -f-  y  t\  +  ^  f  / 

1  After  G.  H.  Darwin.     Article  in  the  Encyclopedia  Britannica 
on  "Tides." 


Mercury  41 


but  -  ^  is  the  diff.  coefficient  of  -  "-^r  with  re- 
gard to  £  that  is  the  diff.  coefficient  of  -  -  ^/  cos  z. 

The  potential  necessary  to  bring  the  Earth  to 
rest  is  then  -  - 7~ £  cos  2. 

The  potential  of  M  with  regard  to  the  particle 
is  — ,  while  the  potential  of  m  upon  the  particle  is 

— plus  a   constant.     This  con- 

\r2  +  p'2  —  2  r  p  cos  z 

stant  we  determine  by  the  condition  that  the  poten- 
tial at  the  planet's  centre  shall  be  zero,  since  we  are 
seeking  the  motion  of  the  particle  relative  to  this 

m  M 

centre,  and  it  becomes    .  .  .    9  — • 

V'    T~  P"  —  2  r  P  cos  % 

Since  r  is  very  large  compared  with  p,  we  may 
advantageously  expand  the  last  in  powers  of  -£-» 
which  gives  :  — 


-     cos  2-    +  etc.]. 

The  first  term  cancels  with  the  potential  for 
bringing  the  Earth  to  rest,  and  we  have  for  the 
whole  potential  urging  the  particle,  — 
M      m 


42  The  Solar  System 

Of  this,  the  first  term  is  the  potential  of  gravity ; 
the  subsequent  ones  the  tide-raising  potential. 

To  get  the  forces,  we  must  differentiate  this 
expression  with  regard  to  the  position  of  the  par- 
ticle. 
Tide-raising       In  order  to  compare  the  tide-raising  forces  on 

force  for  ....  .      _.  ... 

different  different  bodies,  we  will  assume  z  =  o ;  whence 
the  tide-raising  force  at  its  maximum  may  be  ex- 
pressed in  a  rapidly  converging  series,  of  which 

the  first  two  terms  are  ^p*+— ^£- 

If  the  affected  body  be  distant  compared  with 
its  size,  the  first  term  is  enough,  and  we  see  that 
then  the  tide-raising  force  is  directly  as  the  radius 
of  the  second  body,  and  inversely  as  the  cube  of 
its  distance  from  the  first,  while  also  directly  as 
the  latter's  mass. 

But  the  work  done  by  a  force  is  the  product  of 
the  force  into  the  space  through  which  it  acts,  — 
as,  for  instance,  the  lifting  a  weight  a  certain  dis- 
tance, —  and  in  a  given  time  the  space  is  itself 
proportional  to  the  force,  whence  the  work  in  that 
time  is  as  the  square  of  the  force. 

>»o*.*, 

whence  £//2  =  s. 

Whence  if  the  time  remain  constant  the  force  must 

vary  as  the  space.     For  the  proportionate  work 


Mercury  43 


done  in  a  given  time  by  tide-raising  forces,  we  have, 
then,  {^f  -f  ~ir)  >  or  for  most  cases  sufficiently 
well,  taking  only  the  first  term,  4^6P  .  That  is, 

it  is  as  the  square  of  the  attracting  mass  and  the 
square  of  the  radius  of  the  affected  body  directly 
and  inversely  as  the  sixth  power  of  the  latter's 
distance. 


WORK  DONE  BY  TIDE-RAISING  FORCE  IN  UNITY  OF 
TIME  IN  RATIO  TO  SUN'S  ACTION  ON  THE  EARTH 
TAKEN  AS  UNITY. 

By  Sun  on  :  —  4**V  (approx^ 

Mercury     ........  43-26 

Venus         ........  6.60 

Earth          ........  i.oo 

Mars  ......         ...  0.023 

Jupiter        ........  0.006 

f  2  m  p   .    3  m  p2!  2 
On  Earth  by  :  —  [^  +  ^f-  J 

Sun    .....         .  i.oo 

Moon         ........      4-97 


On  Satellites  by  their  Primaries  :  -      [2-^-  -f  ^-^_ 


lapetus      ........       27.6 

Callisto      .......         32,549-° 

Ganymede          .         .....    1,385,600.0 

Moon         ........  2,374.4 


44  The  Solar  System 

Professor  G.  H.  Darwin  has  calculated  the  rela- 
tive effect  of  tidal  retardation  by  the  Sun  on  each 
of  the  several  planets,  that  upon  the  Earth  being 
taken  as  unity,  with  the  accompanying  result :  — 


Planet. 


Number  to  which  Tidal 


Retardation  is  Proportional. 

Mercury 

Venus  

Earth 

Mars 

Jupiter  ...... 

Saturn  ...  . 


Supposing,  then,  all  the  bodies  to  have  started 
in  the  race  for  rotary  retardation  at  the  same  time, 
the  isochronism  of  rotation  and  revolution  of  Mer- 
cury is  what  was  to  have  been  expected.  For 
the  previously  known  facts  were  :  first,  that  the 
Moon  showed  this  state  of  things.  Now  the  rela- 
tive tide-raising  effect  in  a  given  time  of  the  Earth 
on  the  Moon  is  2374  ;  that  of  the  Sun  on  the 
Earth  being  unity.  Second,  that  lapetus  did  the 
same  ;  for  this  satellite  is  always  much  brighter 
on  the  western  side  of  Saturn  than  on  the  eastern. 
Such  a  periodic  change  of  brilliancy  would  be 
accounted  for  by  isochronism  of  rotation  and  revo- 
lution. Now  the  relative  tide-raising  effect  of 
Saturn  on  this  satellite  is  28. 


Mercury  45 


On  the  other  hand,  the  Earth's  rotation  and 
revolution  do  not  coincide  ;  and  the  relative  effects 
of  Sun  and  Moon  on  it  are  :  — 

Sun i.oo 

Moon 4.97 

5-97 

Assuming,  therefore,  that  the  retardation  began 
synchronously  for  all,  Mercury,  upon  whom  the 
effect  was  43,  should  have  reached  the  isochronous 
condition. 

We  may  note  incidentally  that  Venus  on  this 
assumption  falls  in  the  debatable  ground,  since 
the  effect  on  it  is  6.60. 

Bat  we  do  not  know  either  the  time  of  the  birth 
of  the  Moon  nor  the  relative  age  of  the  Earth  and 
Venus.  It  is  quite  possible,  for  aught  we  know, 
that  Venus  may  have  been  subjected  to  the  pro- 
cess practically  much  longer  than  the  Earth. 

It  is  certainly  significant  that  isochronism  ceases 
just  where  a  first  approximation  would  put  it. 

Since  the  date  of  the  detection  of  Mercury's 
isochronism  by  Schiaparelli,  the  third  and  fourth 
satellites  of  Jupiter,  Ganymede  and  Callisto,  have 
been  added  to  the  isochronous  list  by  Mr.  Doug- 
lass at  Flagstaff.  These,  then,  agree  with  theory. 
We  may  safely  predict  that  all  the  other  satellites 


46  The  Solar  System 

of  Jupiter  and  Saturn  will  be  found  to  behave 
similarly. 

Consummation  of  tidal  effect  marks  the  last 
stage  in  the  planetary  career.  So  soon  as  identity 
of  rotation  and  revolution  is  effected,  the  planet 
is  placed  in  a  changeless,  or  largely  changeless, 
state,  which,  so  far  as  we  can  conceive,  means  as 
a  world  its  death.  It  now  turns  the  same  face, 
except  for  libration,  in  perpetuity  to  the  Sun, 
Day  and  night,  summer  and  winter,  have  ceased 
to  exist.  One  half  of  it  is  forever  being  baked, 
the  other  half  forever  frozen  ;  and  from  this  con- 
dition there  is  no  escape.  The  planet  must  remain 
so  until  the  Sun  itself  goes  out. 

Mercury,  therefore,  represents  planetary  de- 
crepitude ;  and  the  symptoms  of  this  old  age  are  : 
loss  of  air ;  isochronous  rotation  and  revolution ; 
rotundity. 


Ill 

MARS 

MERCURY  presents  us  one  phase  of  planetary  Mercury  old; 
development ;  Mars  another,  quite  different.    The  middle  age. 
two  represent  stages  in  world-life  as  distinct  as 
those  of  gray  hair  and  brown  in  human  life. 

Whatever  the  absolute  ages  of  the  several  plan- 
ets, their  relative  ages,  as  measured  intrinsically, 
decrease  pretty  steadily  with  their  distance  from 
the  Sun.  Mercury  is  old ;  Mars,  middle  aged  ; 
Jupiter  young. 

World-life  has  its  earmarks  of  time  as  human 
life  has,  and  betrays  them  quite  as  patently. 

Lack  of  atmosphere,  colorlessness,  changeless 
attitude  toward  the  Sun,  are  the  signs  of  old  age 
in  a  planet.  Mercury  shows  all  these  tokens  of 
senility.  Mars  presents  a  very  different  picture. 

Color  is  a  telltale  trait ;  for  it  is  a  sign  that  sur-   Color  a 

r  ,        ,  ...  T  r  conclusive 

face  development  still  goes  on.     Lack  of  atmos-   criterion. 
phere  alone  prevents  vegetation,  and  this,  coupled 
with  unalterableness  of  face  presented  to  the  Sun, 
weathers  the  surface  to  a  neutral  gray.     Such  a 


48  The  Solar  System 

body  shows  but  the  bleached  bones  of  a  once  living 
world. 

Now  color  is  conspicuously  wanting  on  Mer- 
cury. The  disk  of  the  planet  is  a  chiaroscuro  of 
black  and  white,  tones  devoid  of  tints. 

Mars  a  life-  Mars  is  an  opal.     Colors  comparable  only  to 

wor?d.r  "  that  stone  variegate  its  disk.  At  top  and  bottom, 
collars  of  pearl-white  contrast  vividly  with  light 
areas  of  rose-saffron  and  darker  ones  of  robin's-egg 
blue.  Daylight  reveals  these  colors  much  better 
than  night,  because  the  contrast  of  the  blue-black 
sky  clothes  the  disk  with  yellow  it  does  not  really 
possess,  diluting  the  true  tints. 

Mars  has  The  markings  enable  the  rotation  of  the  planet 

to  be  found-  The  markings  move  under  the  ob- 
server's  eye  and  yet  keep  their  relative  configura- 
tions the  same,  day  after  day  and  year  after  year. 
They  thus  reveal  the  fact  that  the  planet  rotates, 
and  by  the  course  of  their  motion  disclose  the 
axis  about  which  the  rotation  takes  place.  From 
the  observed  data,  spherical  trigonometry  enables 
us  to  fix  this  axis  in  space  and  determine  its  tilt  to 
the  plane  of  the  planet's  orbit.  We  thus  find  that 
it  is  inclined  to  the  Martian  ecliptic  by  an  angle  of 
25°,  and  that  the  solar  day  there  is  24  hours  and  40 
minutes  long.  Thus  Mars  has  both  days  and  sea- 
sons, and  both  days  and  seasons  are  practically 


Mars  49 

counterparts  of  our  own.     The  days  are  a  little  Seasons 

i  •  i  i      accentuated 

longer  and  the  seasons  nearly  twice  as  long,  reck-  much  like 
oned  either  by  Earthly  or  by  Martian  days.     The  °fur^0a 
orderly  succession  of  day  and  night,  spring,  sum-  length. 
mer,  autumn,  and  winter,  are  the  same  there  as 
here. 

Now  this  is  no  accident.  It  is  a  direct  conse- 
quence of  the  planet's  size  and  of  its  position  in 
the  solar  family.  That,  however,  the  circum- 
stances of  the  Earth  and  Mars  should  chance  to 
agree  so  nearly  in  quantity  as  well  as  quality,  we 
as  yet  lack  the  data  to  explain. 

Size,  or  rather  lack  of  it,  has  done  something  Scant 
else  for  Mars.  It  has  reduced  the  atmospheric 
blanket  that  covers  the  planet's  body.  It  did  this 
both  at  the  start  and  subsequently.  If  the  planets 
set  out  with  atmospheres  in  proportion  to  their 
masses,  a  small  planet  having  a  greater  surface  in 
proportion  to  its  mass  would  not  have  this  surface 
so  thickly  covered,  and  its  lesser  gravity  would 
further  spread  this  out  skywards. 

Surface  being  as  4  v  r2,  while  mass  is  as  4  IT  r*,  the  one 
is  to  the  other,  surface  to  mass,  as 


The  ratio  of  surface  to  mass  increases,  therefore,  inversely 
as  the  radius  of  the  body. 


50  The  Solar  System 

In  the  hext  place,  its  gravity  could  control  only 
a  much  smaller  velocity  at  its  surface,  thus  mak- 
ing the  critical  velocity  beyond  which  a  particle 
would  pass  off  into  space  much  less.  By  the  kin- 
etic theory  of  gases,  a  certain  number  of  particles 
will  in  a  given  time  attain  the  critical  velocity,  and 
the  more  the  lower  the  critical  velocity.  Thus, 
from  the  planet  that  hath  not  shall  be  taken  away 
even  that  which  it  hath. 

In  consequence,  on  Mars  the  density  of  the  air 
at  the  surface  of  the  planet  at  the  start  was  prob- 
ably not  denser  than  one-seventh  of  our  own,  or 
more  rare  than  that  at  the  top  of  our  loftiest 
mountains,  and  now  probably  is  rarer  even  than 
this,  owing  to  the  greater  speed  with  which  it  has 
been  lost. 

Rate  of  loss       The  rate  at  which  the  different  gases  would  be 

different         lost  differs.     The  curve  of  probability  shows  that 

they  would  disappear  much  more  rapidly  than  the 

ratio  of  their  speeds.     Water  vapor  would  go  long 

before  atmospheric  air. 

MAXWELL'S  LAW. 

The  possible  values  which  the  components  of  the  mo- 
lecular velocities  can  assume  are  distributed  among  the 
molecules  in  question,  according  to  the  same  law  by  which 
the  possible  errors  of  observation  are  by  the  method  of 
least  squares  distributed  among  the  observations. 


Mars  5 1 


The  number  of  molecules  traveling  at  speed  u  is  given 
by  the  equation,  — 


just  as  the  probability  of  an  error  is  given  by  the  equa- 
tion, — 


VALUES    OF   THE   SPEEDS. 

G  —  mean  value  of  speed  in  metres  per  second. 
G  —  mean  value  of  speed  in  miles  per  second. 

G  G' 

Hydrogen       .....     1838         1.14 

Water  vapor  .....  614  0.38 

Nitrogen         .....  492  0.31 

Atmospheric  air     ....  485  0.30 

Oxygen  ......  461  0.29 

Carbon  dioxide       ....  392  0.24 

Cyanogen        .....  361  0.22 

These  speeds  are  got  from  the  consideration  that  the 
energy,  from  which  follows  the  temperature,  is  the  same  in 
the  two  gases  ;  and,  therefore,  that 


and,  therefore,  the  speed  of  the  molecule  is  inversely  as 
the  square  root  of  the  atomic  weight. 

So  far  theory.     Now  it  is  not  a  little  interesting    Air  on  Mars- 
that  observation  supports  this.     That  air  still  ex- 
ists on  Mars,  oxygen,  nitrogen,  and  carbonic  acid, 


The  Solar  System 


Change  in 
polar  caps. 


Pre-Schiapa- 
rellian  know- 
ledge and 
ideas. 


is  certain  because  of  the  changes  which  we  can 
see  going  on  in  the  surface  markings  ;  for  without 
air  no  change  could  take  place,  and  changes  are 
indisputable.  Water  is  relatively  scarce. 

That  change  goes  on  upon  the  planet's  surface 
has  been  known  for  a  long  time.  The  polar  caps 
were  the  first  telltale.  Sir  William  Herschel,  at 
the  end  of  the  eighteenth  century,  observed  that 
they  waxed  and  waned  periodically,  and  that  their 
period  was  timed  to  that  of  the  planet's  year. 
They  were  therefore  seasonal  phenomena. 

They  behaved  like  ice  and  snow,  and  this  they 
are  generally  supposed  to  be.  Some  astronomers 
find  difficulty  in  conceiving  of  enough  heat  on 
Mars  to  permit  them  to  be  water,  and  carbonic 
acid  has  been  suggested  instead.  But  certain 
phenomena  connected  with  the  melting  prove  that 
carbonic  acid  cannot  be  the  substance.  The  evi- 
dence is  now  very  strong  that  they  are  what  they 
look  to  be,  and  that  the  necessary  heat  will  some- 
how be  explained. 

Up  to  the  time  of  Schiaparelli,  not  much  be- 
yond this  behavior  of  the  polar  caps  and  the  gen- 
eral permanency  of  the  dark  and  light  markings 
was  known  about  the  planet.  Its  physical  con- 
dition was  likened  to  the  Earth's,  the  white 
patches  being  polar  snows,  the  dark  markings 
oceans  and  seas,  and  the  light  markings  land. 


Mars  53 


In  fundamentals,  indeed,  Mars  shows  a  general   Mars  intrinsi- 
similarity  to  the  Earth ;  but  in  subsequent  char-  ^an  the** 
acteristics  it  betrays  a  most  interesting  dissimilar-  Earth- 
ity.     It  is  the  dissimilarity  that  modern  study  has 
specially  brought  out 

The  cause  of  the  dissimilarity  springs  from  the 
planet's  size.  The  less  mass  of  Mars  did  not 
permit  it  initially  to  present  so  fertile  a  field  for 
development.  Mere  size  entirely  alters  physical 
possibilities.  In  the  next  place,  its  dwarfing 
caused  it  to  age  quicker  than  the  Earth. 

Our  knowledge  of  the  planets,  and  especially  of  Schiapareiii's 
Mars,  has  advanced  greatly  within  the  last  quar- 
ter of  a  century.  The  first  steps  of  this  advance 
we  owe,  not  to  instruments,  but  to  the  genius 
of  one  man,  the  Italian  astronomer  Schiaparelli. 
In  1877  he  began  to  observe  Mars,  and  at  once 
showed  a  keenness  of  vision  surpassing  that  of 
any  previous  observer  and  a  susceptibility  to  im- 
pressions surpassing  even  his  acuteness  of  sight. 
It  was  not  so  much  a  matter  of  eye  as  of  brain. 
For  it  turns  out  now,  after  the  fact,  that  several 
of  his  phenomena  had  been  dimly  seen  and  re- 
corded before,  but  without  that  understanding 
which  made  of  them  stepping-stones  to  further  re- 
sults. 

His  object  was  to  map  the  planet  micrometri- 


54  The  Solar  System 

cally.  But  in  the  course  of  his  mapping  he  be- 
came aware  of  some  curious  markings :  dark 
bands  seaming  the  surface  of  the  light  areas,  or 
so-called  continents.  These  he  named  canali,  or 
channels  ;  for  he,  in  company  with  every  one  else, 
at  the  time  believed  the  dark  regions  to  be  seas. 

Having  got  the  hint,  for  it  was  scarcely  more 
than  that,  during  his  first  season,  the  opposition 
of  1877,  he  then  showed  that  element  of  genius 
without  which  very  little  is  ever  accomplished, 
the  persistence  to  follow  up  a  clue.  As  Mars 
came  round  again  he  attacked  the  planet  in  the 
light  of  what  he  had  already  learnt,  and  first  con- 
firmed and  then  extended  his  discovery.  This  he 
continued  to  do  at  each  succeeding  opposition. 
The  more  he  studied,  the  stranger  grew  the  phe- 
nomena he  detected.  And  it  is  to  his  everlasting 
credit  that  he  did  this  in  the  face  of  the  skepti- 
cism and  denial  of  practically  the  whole  astro- 
nomic world.  He  won.  The  voices  that  ridiculed 
him  are  all  silent  now.  To-day  the  canals  of 
Mars  are  well-recognized  astronomic  facts,  and 
constitute  one  of  the  most  epoch-making  astro- 
nomic discoveries  of  the  nineteenth  century. 

Through  a  complete  cycle  of  oppositions,  that  is, 
from  the  nearest  to  the  most  remote  and  round  to 
the  nearest  again,  a  period  of  fifteen  years,  Schia- 


Mars  55 

parelli  continued  to  study  these  curious  phe- 
nomena, having  them  practically  all  to  himself,, 
Indeed,  his  grand  isolation  in  the  quest  makes 
one  of  the  finest  and  saddest  chapters  in  the  his- 
tory  of  discovery.  In  the  course  of  these  solitary 
years  he  came  to  see  the  canals  better,  and  they 
grew,  on  improving  acquaintance,  steadily  more 
strange.  He  found  that  they  were  far  more  reg- 
ular than  he  had  at  first  thought,  and  he  noted 
that  they  were  dependent  in  appearance  upon  the 
season  of  the  planet's  year.  So,  likewise,  were 
the  large  dark  markings,  and  he  attributed  the 
behavior  of  both  to  a  seasonal  shift  of  water  over 
the  surface. 

His  theory  of  the  planet's  physical  condition, 
derived  from  his  observations,  was  as  follows : 
that  the  polar  caps  were  ice  and  snow ;  that  the 
blue-green  areas  were  seas  and  the  reddish-ochre 
ones  land;  that  the  canals  were  natural  water- 
channels  or  straits  honeycombing  the  land  and 
cutting  it  up  into  a  patchwork  of  large  islands,  a 
sort  of  natural  Venice  on  a  world-wide  scale ;  and 
finally  that  the  surface  was  subject  to  annual  or 
semiannual  inundations  and  dryings-up,  timed  to 
the  melting  of  the  polar  caps. 

Schiaparelli  retired  practically  in  1892,  though 
not  formally  till  a  little  later.  His  work  was  taken 


56  The  Solar  System 

up  by  other  hands,  and  the  impetus  he  gave  the 
matter  has  resulted  in  a  knowledge  of  Mars  which 
has  quite  revolutionized  even  the  conception  he 
bequeathed  of  the  planet. 

Methods  of       Before  proceeding  to  post-Schiaparellian  work, 
iervation.  .  interest  you  to  know  how  the  phenomena 


in  question  have  been  detected,  and  what  they 
look  like  when  seen. 

Contrary  to  what  the  layman  thinks,  the  size 
of  the  instrument  is  the  least  important  factor  in 
the  process.  As  in  most  things,  the  man  is  the 
essential  machine  ;  and  next  in  desirability  to  the 
presence  of  man  is  the  absence  of  atmosphere. 
In  good  air,  with  fair  attention,  the  canals  are  not 
very  difficult  objects.  Indeed,  the  surprise  is  that 
they  were  not  detected  long  ago.  Under  suitable 
atmospheric  conditions  a  four-inch  glass  will  show 
them  perfectly.  Steady  air  is  one  essential  ; 
steady  study  another. 

The  canals.  In  appearance  they  are  unlike  any  other  phe- 
nomena presented  in  the  heavens.  Pale  pencil 
lines,  deepening  on  occasion  to  India  ink,  seem  to 
cobweb  the  continents.  Their  tone  depends  on 
the  seeing,  in  the  first  place,  and  on  the  season, 
in  the  second.  Their  width  is  invariable  through- 
out, and  their  directness  something  striking. 
Measurable  width  they  have  not  ;  it  is  only  by 


m 


58  The  Solar  System 

depth  of  tint  that  their  importance  is  inferred. 
But  their  most  amazing  attribute  is  their  geomet- 
ric character.  They  seem  to  be  generally  arcs  of 
great  circles  drawn  from  certain  salient  points  on 
the  planet's  surface  to  certain  other  equally  salient 
ones. 

Their  number  appears  to  be  legion.  Schiapa- 
relli  discovered  104.  But  the  better  the  planet  is 
seen  the  more  of  them  come  out.  About  350 
have  now  been  mapped  at  Flagstaff,  and  the  num- 
ber is  only  limited  by  our  penetration.  Like  the 
asteroids,  the  larger  ones  have  already  been  de- 
tected. Each  opposition  now  brings  out  smaller 
and  smaller  specimens. 

Their  But   now  comes  a  most  interesting  fact  con- 

character  nected  with  them  which  was  discovered  by  Schia- 
parelli  and  found  equally  true  at  Flagstaff.  They 
are  not  always  equally  visible.  Sometimes  they 
are  conspicuous,  sometimes  scarcely  discernible 
even  to  a  practiced  eye.  And  this  is  not  mere 
matter  of  distance.  The  best  time  for  seeing  the 
planet  is  not  the  best  time  for  detecting  the 
canals. 

At  certain  oppositions  we  pass  the  planet  at 
close  quarters,  at  certain  others  a  good  way  off. 
The  close  approaches  are  called  favorable  opposi- 
tions, the  distant  encounters  unfavorable  ones. 


Mars  59 

But  the  latter  are  not  so  unfavorable  as  they  are 
thought.  For  another  factor  beside  nearness  af- 
fects the  reckoning.  The  planet's  axis  is  tilted  to 
the  plane  of  its  orbit  at  an  angle  of  25°,  and  is  so 
faced  that  the  southern  hemisphere  is  presented 
to  us  at  the  time  of  closest  approach.  Now  the 
canals  lie  chiefly  in  the  northern  hemisphere.  In 
the  next  place,  it  is  then  the  northern  winter, 
and  careful  comparison  reveals  the  fact  that  the 
conspicuousness  of  a  canal  is  a  function  of  the 
Martian  time  of  year,  becoming  pronounced  in 
summer  and  fading  out  in  winter. 

This  is  one  reason  why  the  canals  so  long 
eluded  astronomers.  They  were  not  looked  for 
at  the  proper  time. 

The  first  important  post-Schiaparellian  advance   «  seas "  not 
was  made  in  the  dark  regions  of  the  planet. 

For  two  centuries  the  dark  regions  were  held 
to  be  seas.  It  became  evident,  however,  from 
Pickering's  observations  in  1892  that  the  great 
part  of  them  could  not  be  such.  In  1894,  at 
Flagstaff,  it  further  became  evident  that  no  part 
of  them  could  be  water.  From  the  way  in  which 
the  clarification  of  the  dark  regions  progressed 
with  the  planet's  seasons,  it  had  become  patent 
that  the  bodily  transference  of  substance,  such, 
for  instance,  as  water,  from  one  place  to  another, 


seas. 


60  The  Solar  System 

could  not  account  for  the  phenomena.  For  the 
decrease  in  one  locality  was  not  offset  by  the  in- 
crease in  others.  As  the  quantity  of  the  change, 
positive  and  negative,  did  not  balance,  the  change 
could  not  be  due  to  a  shift  of  matter.  It  must, 
therefore,  be  ascribable  to  a  transformation  of 
matter.  And  the  only  thing  of  suitable  conduct 
and  proper  local  color  to  show  the  phenomena 
was  vegetation.  The  "  seas  "  were  not  seas,  but 
probably  areas  of  vegetation. 

Oases.  The  next  significant  discovery  was  the  detec- 
tion of  the  oases,  or  small  round  black  spots  that 
dot  the  planet's  surface.  These  were  initially  seen 
as  such  by  W.  H.  Pickering,  at  Arequipa,  in  1892. 
Pickering  called  them  lakes,  but  for  a  reason 
which  will  appear  later  it  seems  more  proper  to 
consider  them  oases.  Quite  as  singular  a  feature 
as  the  canals,  they  prove  to  be  as  universal  a  one. 
They  are  the  more  difficult  of  detection ;  which 
is  the  reason  they  were  recognized  later.  Schia- 
parelli  told  the  writer  that  he  had  himself  sus- 
pected them,  but  could  not  make  sure. 

Just  as  the  canals  form  a  mesh  over  the  disk, 
so  the  oases  make  the  knots  where  the  lines  of 
the  network  cross.  To  them,  in  short,  the  canals 
rendezvous.  The  number  of  lines  which  thus 
come  together  at  one  and  the  same  point  is  some- 


Mars  6 1 


times  considerable.  Nine  meet  at  the  Phoenix 
lake,  eleven  at  the  Trivium  Charontis,  and  no  less 
than  seventeen  at  the  Ascraeus  Lacus  at  the  top 
of  Ceraunius.  Nor,  so  far  as  can  be  seen,  is  any 
important  junction  without  its  spot.  Their  bear- 
ing upon  the  explanation  of  the  canals  is  at  once 
evident. 

In  character  the  oases  are,  when  well  seen,  very 
small  and  very  dark.  Too  small  to  disclose  dis- 
tinctive color,  they  are  the  most  deeply  complex- 
ioned  detail  upon  the  disk,  and  presumably  blue. 
It  is  only  in  poor  air  that  they  show  large  and 
diffuse.  About  three  degrees  in  diameter  and 
seemingly  quite  round  as  a  rule,  they  must  be 
100  miles  across,  and,  for  all  their  minuteness, 
cover  a  goodly  area  of  ground. 

They  seem  to  share  the  same  seasonal  transfor- 
mation with  all  the  other  markings. 

The  next  step  was  the  discovery  of  canals  in  Canals  and 

, ,        ,     ,  .  r   A ,          ,  ~          1-1  oases  in  the 

the  dark  regions  of  the  planet.  Streaks  in  these  dark  regions, 
regions  were  seen  in  1892  at  Arequipa  and  at  the 
Lick  Observatory,  much  as  Dawes  had  seen 
streaks  in  the  light  ones  thirty  years  before.  But 
in  1 894,  at  Flagstaff,  Mr.  Douglass  found  that  the 
streaks  were  not  irregular  markings,  but  a  sys- 
tem of  lines  possessing  the  same  singular  char- 
acteristics which  distinguish  and  differentiate  the 


62  The  Solar  System 

"canals"  in  the  light  regions  from  other  celestial 
phenomena.  In  short,  he  detected  in  the  dark 
regions  what  Schiaparelli  had  detected  in  the 
light.  Counterparting  exactly  the  network  over 
the  light  areas,  a  mesh  of  similar  lines  overspread 
the  blue-green  areas.  The  lines  were  of  uniform 
width,  of  unswerving  directness,  and  went  from 
definite  points  to  other  equally  determinate  ones. 
These  points  were  always  of  geographic  impor- 
tance. They  were  at  the  ends  of  "  seas,"  at  the 
bottom  of  "bays,"  or  at  points  on  the  "coast- 
line" where  canals  debouched.  The  lines  con- 
nected these  topographical  centres,  crossing  one 
another  in  the  process,  and  at  the  junctions  there 
showed,  just  as  in  the  light  areas,  dark  round 
spots. 

Instantly  to  be  deduced  from  such  engraving 
was  that  the  "  seas  "  were  not  bodies  of  water. 
We  knew  this  already,  as  I  have  shown ;  but  the 
evidence  was  valuable  in  completely  convincing 
those  who  require  more  than  mediate  proof.  Per- 
manent lines  cannot  be  writ  on  water.  The  seas 
lost  their  character  forever. 

The  absence  of  any  bodies  of  water  outside  of 
the  temporary  polar  sea  introduces  a  far-reaching 
difference  between  Mars  and  the  Earth.  On 
Earth  three  quarters  of  the  surface  is  water ;  on 


Mars  63 


Mars  all  is  land.  Instead  of  having  more  sea 
than  it  can  use,  the  planet  must  be  in  straits  for 
the  article.  Its  whole  supply  comes  from  the 
annual  melting  of  the  polar  caps. 

The  canal  system  of  the  dark  regions  not  only 


" 


ir<  /loRTh  PoLAR  CAP.  JA/H  1*5)01  CABALS  JU/HE 

\*r  ~\~i* 

8HOW1/1Q  THE     !De/1TITY  OF  THE    TYYO.. 


FIG.  IX. 


64  The  Solar  System 

Two  systems,  resembles  the  system  in  the  light ;  the  one  joins 
on  to  the  other.  The  points  where  the  system  in 
the  light  areas  strike  the  dark  are  the  points  from 
which  the  canals  in  the  dark  regions  set  out.  The 
two  are  thus  but  parts  of  one  world-wide  whole. 
Whatever  purpose  the  one  subserves  is  thus  taken 
up  and  extended  by  the  other. 

Nor  does  the  communication  come  to  an  end  in 
the  dark  regions.  From  the  southern  portions  of 
these,  in  the  southern  hemisphere,  other  canals 
run  straight  into  the  polar  cap ;  in  the  northern 
hemisphere,  similarly,  canals  penetrate  to  the  most 
northern  limit  of  the  snow. 

Lastly,  the  rifts  which  appear  in  the  caps  during 
the  process  of  melting  turn  out  to  be  where 
subsequently  are  seen  canals.  Now,  as  there 
are  no  mountains  on  Mars,  differences  of  level 
cannot  be  a  cause  of  melting ;  areas  of  vegetation 
could. 

Summation.  We  may  sum  up  our  present  knowledge  of  the 
surface  conditions  of  the  planet  as  follows  :  — 

(1)  Change  takes  place  upon  the  planet's  sur- 
face ;  this  proves  the  presence  there  of  an  atmos- 
phere. 

(2)  The  limb-light,  the  apparent  evidence  of  a 
twilight,  and  the  albedo,  all  point  to  a  density  for 
this  atmosphere  very  much  less  than  our  own. 


Mars  65 


(3)  The  polar  caps  melt  in  their  summer  and 
accumulate  in  their  winter,  thus   showing  them- 
selves to  be  seasonal  in  character. 

(4)  As  they  melt,  they  are  bordered  by  a  blue 
belt,  which  retreats  with  them.     This  negatives 
carbonic  acid  as  the  substance  composing  them, 
and  leaves  to  our  knowledge  only  water  as  a  possi- 
ble explanation. 

(5)  Their  extensive  melting  shows  their  quan- 
tity to  be  inconsiderable,  and  points  to  a  dearth  of 
water. 

(6)  Comparison     with     previous    observations 
shows  the  melting  to  occur  in  the  same  consecu- 
tive places  year  after  year.     The  melting  is  thus 
a  thing  which  can  be  locally  counted  on. 

(7)  The  greatest  local  melting  is  just  south  of 
the  largest  dark  (blue-green)  regions,  the  bays  in 
the  polar  sea  in  these  longitudes  being  the  largest. 

(8)  The  dark  regions  are  subject  to  a  wave  of 
seasonal  changes  ; 

(9)  which  follows  upon  the  melting  of  the  cap. 
They  darken  in  early  summer  and  fade  out  in 
their  autumn. 

(10)  The  dark  regions  are  not  seas  :  first,  be- 
cause in  Professor  W.  H.  Pickering's  experiments 
their  light  showed  no  trace  of  polarization,  while 
that  of  the  polar  sea  did  ; 


66  The  Solar  System 

(n)  second,  because  the  quantity  of  the  dark- 
ening is  not  offset  by  the  synchronous  lightening 
elsewhere.  It  cannot  therefore  be  due  to  shift  of 
substance  ; 

(12)  third,  because  they  are  seamed  by  a  canal 
system  counterparting   that  of   the   light   areas, 
permanent  in  place. 

(13)  Extension  of  this  shows  that  there  are  no 
permanent  bodies  of  water  on  the  planet. 

(14)  All  the  phenomena  are  accounted  for  by 
supposing  them  to  be  areas  of  vegetation. 

(15)  The  polar  sea  being  a  temporary  affair,  the 
water  from  it  is  fresh. 

(16)  Observations  on  the  terminator  reveal  no 
mountains  on  Mars,  the  details  of  the  observa- 
tions being  incompatible  with  such  supposition  ; 

(17)  but   do  reveal  apparently  clouds,   which, 
however,  are  rare,  and  are  chiefly  visible  at  sunrise 
and  sunset, 

(18)  and  seem  connected  with  the  heat  equator. 

(19)  The   bright   areas   look   and   behave  like 
deserts. 

(20)  In  their  winter,  the  south  temperate  light 
regions  are  covered  by  a  white  veil,  which  may  be 
hoar-frost  or  may  be  cloud. 

(21)  Very  brilliant  patches  appear  also  in  the 
equatorial  light  regions  that  last  for  weeks,  and 
seem  independent  of  diurnal  conditions. 


Mars 


67 


Conclusions 
as  to 
physical 


(22)  They  appear  always  in  the  same  places. 

(23)  A  spring  haze  surrounds  the  polar  caps 
during  certain  months,  outside  of  and  distinct  from 
the  cap  itself. 

(24)  A  progressive  change  of  darkening  sweeps 
over  the  planet's   face  from  pole  to  pole  semi- 
annually,  beginning  with  the  cap,  and  developing 
as  vegetation  would  down  the  disk. 

These  phenomena  lead  to  the  conclusion  that 
the  polar  caps  are  masses  of  snow  and  ice ;  that 
the  light  areas  are  deserts ;  that  the  blue-green  condition 
areas  are  tracts  of  vegetation ;  that  there  are  no 
permanent  bodies  of  water  on  the  planet,  and 
very  little  water  in  any  form  ;  that  the  surface  is 
remarkably  flat ;  that  the  temperature  is  moder- 
ately high  by  day  but  low  at  night ;  that  it  is 
fairly  warm  in  summer  but  cold  in  winter ;  and 
that  the  seasonal  change  of  the  vegetation  is 
marked  even  at  our  distance  away. 

To  these  conclusions  we  are  led  by  the  general 
aspect  and  behavior  of  the  planet's  disk.  We 
have  reached  them  without  reference  to  the  canals 
considered  in  themselves,  and  we  should  continue 
to  put  faith  in  them  were  the  canals,  with  all 
their  strange  characteristics,  blotted  from  exist- 
ence. Unbeholden,  then,  to  the  canals  for  this  con- 
clusion, we  are  the  more  impressed  to  find  that  the 


68  The  Solar  System 

supposition  that  the  "canals"  are  not  the  result 
of  chance  falls  completely  in  line  with  our  result. 

Water  is  very  scarce  on  the  planet,  and  is  abso- 
lutely essential  to  life.  Vegetation  exists  there, 
and  it  is  therefore  highly  probable  that  organic 
life  is  to  be  found  there,  too.  This  becomes  a 
posteriori  probable,  when  we  behold  a  system  of 
lines  inexplicable  on  any  other  ground  and  pre- 
cisely what  would  be  needed  for  the  diffusion  of 
water  over  the  planet's  surface. 

What  we  find  is  this  :  — 

(25)  A  network  of  fine  dark  lines  meshing  the 
deserts. 

(26)  The  lines  are  uniform  throughout  and  from 
five  to  thirty-five  miles  in  width,1 

(27)  and    hundreds,    sometimes   thousands   of 
miles  long, 

(28)  usually,    if  not   always,  following  arcs  of 
great  circles, 

(29)  starting    from   topographically   important 
points  in  the  dark  regions, 

(30)  and  traveling  to  other  equally  conspicuous 
points ; 

(3 1)  both  terminals  show  dark  spots,  a  caret  in  the 
coastline  and  what  seems  around  spot  in  the  desert ; 

1  Tests  by  the  writer  on  telegraph  lines  show  that  a  line  can 
be  seen,  owing  to  its  length,  when  its  width  is  2".$,  to  the  naked 
eye.  This  would  mean  about  5  miles  on  Mars. 


Mars  69 


(32)  all    the   way   from    three    to    seventeen 
"  canals  "  will  converge  upon  the  same  spot ; 

(33)  the  spots  are  perhaps  a  hundred  miles  in 
diameter,  and  their  number  is  very  great ; 

(34)  the  dark  regions  are  meshed  by  a  similar 
network  ; 

(35)  the   points  of  departure  of   both  are  the 
same; 

(36)  similar  centring  spots  show  in  the  dark 
areas,  darker  than  their  background  ; 

(37)  with   the  dark  network   "canals"  others 
connect,  running  to  the  edge  of  the  extreme  melt- 
ing limits  of  both  caps ; 

(38)  the  lines  are  seasonal  phenomena,  develop- 
ing after  the  melting  of  their  respective  polar  cap 
and  fading  out  later  ; 

(39)  those  in  the  polar  regions  occupy  the  place 
of  earlier  rifts  in  the  snow-field,  as  if  the  ground 
were  there  thawed  by  vegetation. 

They  are  of  uniform  width ;  that  is,  they  waste 
nothing  in  breadth.  Whatever  breadth  is  neces- 
sary is  used,  and  no  more,  and  that  is  retained 
throughout.  They  go  directly  from  certain  con- 
spicuously probable  points  to  certain  others.  If 
we  were  obliged  to  connect  the  planet  by  a  sys- 
tem of  intercommunication,  it  is  precisely  those 
points  we  should  ourselves  select. 


70  The  Solar  System 

In  addition  to  the  departure  points  on  the  bor- 
ders of  the  dark  regions  which  are  provided  by 
nature  are  a  host  of  others  not  apparently  so  origi- 
nated. These  are  the  round  black  dots,  —  the 
oases.  They  are  found  at  the  intersections  of 
the  lines.  How  important  they  are  in  the  planet's 
economy  is  to  be  inferred  from  the  host  of  canals 
each  of  them  receives.  Four,  very  rarely  three, 
is  the  minimum  number  of  approaches  or  depar- 
tures from  them,  and  this  number  rises  in  the  case 
of  Ceraunius  to  seventeen.  Even  London  hardly 
has  this  number  of  railway  lines  entering  and 
leaving  it.  It  is  not  too  much  to  suppose,  though 
as  yet  we  cannot  count  it  more  than  a  conjecture, 
that  the  oases  serve  some  such  purpose  as  our 
cities  and  are  centres  of  population. 

From  this,  we  add  to  our  list  of  conclusions,  — 
that  the  canals  are  artificial,  and  therefore  imply 
organic  intelligent  life  upon  the  planet. 

Our  synthesis  leads,  then,  to  the  conclusion 
that  Mars  is  circumstanced  like  ourselves  in  the 
midway  of  planetary  existence,  but  that  the  planet 
has  advanced  further  on  the  road  to  old  age  and 
death  than  we  have  yet  done. 

That  its  world-life  was,  in  any  but  the  broadest 
sense,  an  analogue  of  our  own,  is  certainly  not  the 
case.  Its  career  began  under  different  physical 


Mars  71 

conditions,  owing  to  its  size,  ran  more  rapidly 
through  its  successive  stages,  again  owing  to  its 
size,  and  will  come  to  an  end  sooner  for  the  same 
reason. 

As  a  detail  of  this,  life  on  Mars  must  take  on 
a  very  different  guise  from  what  it  wears  on 
Earth.  It  is  certain  that  there  can  be  no  men 
there  ;  that  is  as  certain  as  anything  well  can  be. 
But  this  does  not  preclude  a  local  intelligence 
equal  to,  and  perhaps  easily  superior  to,  our  own. 
We  seem  to  have  evidence  that  something  of  the 
sort  does  exist  there  at  the  present  moment,  and 
has  made  imprint  there  of  its  existence  far  exceed- 
ing anything  we  have  yet  left  upon  mother  Earth. 

In  conclusion,  let  me  warn  you  to  beware  of 
two  opposite  errors ;  of  letting  your  imagination 
soar  unballasted  by  fact,  and,  on  the  other  hand, 
of  shackling  it  so  stolidly  that  it  loses  all  incentive 
to  rise.  You  may  come  to  grief  through  the  first 
process ;  you  will  never  get  anywhere  by  the 
second.  Take  general  mechanical  principles  for 
compass  and  then  follow  your  observations.  Im- 
agination is  as  vital  to  any  advance  in  science  as 
learning  and  precision  are  essential  for  starting 
points. 


IV 

SATURN    AND    ITS    SYSTEM 

Saturn.  SATURN  marked  to  the  ancients  the  outer  bound- 

ary of  the  solar  system.  From  its  slow  motion, 
they  rightly  conjectured  it  to  be  the  farthest  away 
of  all  the  "wanderers,"  and  wrongly  to  be  sinister 
in  intent.  Our  word  "saturnine"  expresses  the 
feeling  it  inspired. 

In  the  telescope,  Saturn  is  undoubtedly  the 
most  immediately  impressive  object  in  the  hea- 
vens. Few  persons  can  be  shown  the  planet  for 
the  first  time  without  an  exclamation.  To  see  it 
sail  into  the  field  of  view,  its  great  ball  diademed 
by  an  elliptic  ring,  and  carrying  with  it  a  retinue 
of  star-points  set  against  the  blue-black  back- 
ground of  the  sky,  gives  the  most  prosaic  a  sensa- 
tion. 

Saturn's  self  we  shall  leave  till  we  come  to 
speak  of  Jupiter  (in  the  next  chapter) ;  and  shall 
here  consider  the  two  systems  of  bodies  dependent 
on  it,  —  its  rings  and  its  satellites. 

The  Unique,  so  far  as  we  know,  is  that  appanage 

of  Saturn  which  makes  the  planet  so  superb  a 


Saturn  and  its  System  73 

sight,  —  the  ring  system.  It  baffled  Galileo  with 
his  opera-glass,  who  first  saw  the  planet  triform, 
and  then,  to  his  surprise,  marked  the  two  smaller 
bodies  disappear,  as  if  Saturn  had  indeed  eaten 
his  offspring. 

Crowning  the  planet's  equator  are  several  con- 
centric flat  rings  of  light.  Three  are  usually 
distinguished,  known  as  A,  the  outer  ring  ;  B,  the 
middle  ring ;  and  C,  the  inner  or  dusky  ring.  The 
outer,  A,  has  an  extreme  radius  of  about  85, 700 
miles.  It  is  12,000  miles  across,  and  is  separated 
from  B  by  a  dark  space  3400  miles  wide,  known 
as  Cassini's  division.  B,  the  broadest  and  bright- 
est of  the  rings,  is  17,000  miles  in  width,  and  is 
joined  without  perceptible  interval  by  C,  which  is 
much  fainter,  resembling  a  crepe  veil  stretched 
from  the  inner  edge  of  B,  9500  miles  toward  the 
planet,  from  whose  limb  it  is  sundered  by  a  gap  of 
between  7000  and  8000  miles. 

Two  thirds  way  from  the  outer  to  the  inner 
edge  of  A  is  another  division  or  dark  line,  much 
narrower  than  Cassini's,  and  sometimes  nearly 
invisible,  known  as  Encke's  division,  though  sus- 
pected before  by  Short. 

Edward  Roche,  in  1848,  was  the  first  to  show  Constitution 

of  the  rings. 

that  the  rings  were  composed  of  discrete  par- 
ticles, —  mere  dust  and  ashes.  He  drew  this  con- 


74  The  Solar  System 

sequence  directly  from  his  investigations  on  the 
minimum  distance  a  small  fluid  satellite  may  safely 
approach  a  fluid  primary ;  for  within  a  certain  dis- 
tance the  differential  or  tidal  pull  of  the  planet 
must  disrupt  the  satellite.  This  distance  is  called 
Roche's  limit. 

For  equal  densities  of  planet  and  satellite, 
Roche's  limit  is  2.44  times  the  planet's  radius  ; 

for  unequal  densities,  as   \—  x  244,  where  d  is 

the  density  of  the  primary ;  d'  of  the  satellite. 

Saturn's  system  offers  the  only  instance  where 
matter  circulates  within  the  limit,  and  Roche 
stated  distinctly  that  the  rings,  therefore,  must 
be  mere  meteoric  stones. 

Even  Laplace  had  shown  that  the  rings  must 
be  broken  up  for  stability's  sake  into  several  nar- 
row ones,  each  revolving  at  its  own  rate.  Pierce 
proved  that  they  could  in  no  case  be  solid.  Max- 
well then  demonstrated  that  they  could  not  be  so 
much  as  liquid,  as  disrupting  waves  would  be  set 
up,  but  must  consist  of  a  swarm  of  small  bodies,  - 
brickbats  he  likened  them  to,  —  each  pursuing  its 
own  path.  What  the  spectroscope  in  Keeler's 
ingenious  hands  made  visible  to  the  eye  had 
thus  been  known  to  mechanics  from  the  time  of 
Laplace. 


Saturn  and  its  System  75 

These  flights  of  small  bodies  are  so  exactly  in  AH  in  the 
one  plane  that  they  vanish  when  the  rings  are  s 
turned  edgewise  to  the  Earth.  Their  lustre  shows 
them  to  be  relatively  densely  packed,  so  that  colli- 
sions among  them  must  be  not  infrequent.  In 
consequence  of  this,  Maxwell  predicted  that  they 
would  eventually  be  forced  both  out  or  in,  and  in 
part  fall  upon  the  ball,  in  part  be  driven  farther 
from  the  planet.  Certainly  such  must  ultimately 
happen  ;  but  the  evidence  is  not  conclusive  that 
either  process  has  yet  been  observed. 

•The  spectroscope  shows  that,  unlike  Saturn,  No  air  about 
they  carry  no  air  with  them.  This,  from  their 
minute  size,  was  to  be  expected  on  the  kinetic 
theory  of  gases  and  the  clever  deduction  from  it 
as  to  the  atmosphere  a  body  may  retain,  made  by 
Johnstone  Stoney. 

To  attempt  to  account  for  their  dimensions  and  Gaps  in  them, 
divisions  might  at  first  seem  hopeless.  Why  A  is 
made  up  of  an  outer  and  an  inner  portion  parted 
by  Encke's  streak ;  why  B  is  sundered  from  A  by 
Cassini's  division  ;  and  why  C  is  sharply  con- 
trasted with  B  at  its  inner  edge,  sound  like  difficult 
questions.  But  nothing  in  celestial  mechanics  is 
the  outcome  of  chance,  and  this  is  no  exception  to 
the  rule. 

To  begin  with,  Roche's  limit  falls  just  at  the 


76  The  Solar  System 

Roche's  limit,  outer  edge  of  the  system,  supposing  the  density 
of  the  satellite  to  be  f  of  the  primary's.  Now 
the  satellites  of  Saturn  are  certainly  a  little  denser 
than  the  planet.  From  our  present  values  of  its 
mass  and  volume,  Titan's  density  comes  out  .24. 
This,  then,  is  what  has  limited  the  system  ex- 
ternally. 

For  the  rest  of  it,  another  force  has  proved 
fashioner. 

Commensu-          Our  mathematics    do  not   permit  us   to  solve 
rate  periods. 

rigorously  the  problem  of  three  bodies  ;  that  is, 

the  motion  of  a  first  revolving  round  a  second  and 
perturbed  by  a  third.  We  have  to  have  recourse 
to  approximations  in  series.  We  can  thus  deter- 
mine to  any  degree  of  accuracy  the  result.  Now 
the  perturbative  effect  produced  by  a  third  body 
upon  the  major  axis  of  a  second  revolving  in  its 
own  plane  may  be  expressed  by  a  series  developed 
in  terms  depending  on  powers  of  the  eccentricity 
and  cosines  of  multiple  arcs  of  the  mean  motions. 
The  typical  form  of  one  of  these  terms  is 


COS         -    »  ~ 


where  P  is  a  function  of  a  and  a',  the  radii  vectores. 
From  this,  it  appears  that  if  /  and  q  are  nearly  in 
the  inverse  ratio  of  the  mean  motions, 
pn  —  qn'  is  nearly  o, 


Saturn  and  its  System  77 

and  the  term  has  a  large  coefficient,  and  therefore 
a  large  value. 

If,  then,  the  mean  motions,  and  therefore  the 
periods,  of  perturber  and  perturbed  are  commen- 
surable, the  disturbing  effect  upon  the  major  axes 
of  each  will  be  great.  The  major  axes  will  be 
altered  until  the  periods  cease  to  be  commensura- 
ble, and  it  will  be  long  before  perturbation  brings 
them  back  to  commensurability  again. 

Furthermore,  the  least  value  /  -f-  in  can  have  is  Greatest 
p  —  q,  while  the  period  of  the  action  of  the  term  the  smallest 

ratio. 

is  .    _     , ;  whence  the  greatest  term  is  when/ 

and  q  are  both  as  small  as  possible,  since  conjunc- 
tions will  occur  oftener  in  proportion  as  q  is  small. 

Geometrically,   the   effect  can  be  seen  in  the  Effect 

r   n  /-i        i        ^         j-  4.      -u-  11     •      geometrically 

following  way.  Clearly,  the  disturbing  pull  is  considered, 
greatest  when  the  two  bodies  are  in  conjunction, 
and  so  long  as  the  periods  are  incommensurable, 
conjunctions  will  occur  in  different  parts  of  the 
orbit  successively,  and  thus  neutralize  one  an- 
other's effect  upon  the  major  axes.  But  if  the 
periods  of  the  two  bodies  be  commensurable,  con- 
junctions will  occur  in  the  same  place  over  and 
over  again,  and  the  major  axes  will  be  altered 
there  without  compensatory  alterations  elsewhere  ; 
and  this  will  go  on  until  the  major  axes  are  so 


78  The  Solar  System 

altered  that  commensurability  of  period,  which 
depends  on  the  major  axis,  ceases.  Then  the 
bodies  will  cease  to  affect  each  other  forcibly. 
They  will  gradually  meet  each  other  elsewhere, 
finally  oppositely  to  what  they  did  at  first,  and 
the  action  first  produced  will  be  as  gradually  un- 
done ;  but  it  will  be  very  long  before  the  major 
axes  attain  their  original  value  again ;  then  they 
will  pass  rapidly  through  them  once  more  in  the 
reverse  way. 

If,  then,  the  periods  of  the  two  bodies  are  com- 
mensurable, they  will  not  appear  to  be  so,  since 
their  major  axes  will  stay  commensurate  but  a 
brief  time  compared  with  the  time  they  are  out. 
Gaps  due  to  Now,  if  we  have  a  swarm  of  bodies  revolving 
at  vari°us  distances  round  a  central  mass,  and 
disturbed  by  a  third,  the  third  will  seem,  in  con- 
sequence of  this,  to  sweep  out  spaces  where  other- 
wise bodies  would  revolve  in  times  commensurate 
with  its  own.  Jupiter  has  done  this  very  thing  in 
the  case  of  the  asteroids,  striping  the  zone  with 
vacant  belts.  Calculation  alone  reveals  this,  as 
the  asteroids  are  too  few  to  disclose  the  fact  to 
the  eye.  But  in  the  rings  of  Saturn  we  can  ac- 
tually see  the  empty  places.  The  gaps  in  the 
rings  are  shown  in  the  following  table  and  in  the 
accompanying  picture  of  the  ring  system  :  - 


Saturn  and  its  System 


79 


FIG.  X.    SATURN'S  RINGS. 


Outer  radius  outer  ring  A 
Encke's  division  .  . 

Inner  radius  outer  ring  A 
Cassini's  division  .  . 

Outer  radius  ring  B     .     . 

Inner  radius  ring  B     .     . 

Outer  radius  ring  C     .     . 

Inner  radius  ring  C     .     . 

Planet  radius  . 


Old 
Determination. 


54000 
74000 

72400 
56200 
56200 
46700 
37500 


New 
Determination. 


80000 


73200 


85700 
75300 

71900 
54700 
54700 
43900 
37000 


SlOIO 


73620 


Let  us  note  these  gaps  and  edges  and  then  cal-  Gaps 
culate  what  perturbing  effect  the  satellites  would 
exert.     The  satellites  which  would  have  the  great- 


8o  The  Solar  System  ' 

est  perturbative  action  on  the  rings  is  Mimas,  his 
effect  being  more  than  three  times  that  of  Encel- 
adus  and  more  than  twice  that  of  Tethys. 
The  equations  of  motion  are  for  x  — 

d^x  _          x     ,    m'  (x'  —  x]        m' x' 

~dp   r      -73-         (r'  —  r}'6    '     ~~r^' 

of  which  the  first  is  the  direct  force  of  the  central  body, 

whose  mass  is  taken  as  i,  upon  mj  and  the  other  terms 

are  the  perturbing  force  of  m'  on  m. 

Assuming  the  three  to  be  in  conjunction,  this  last  be- 
comes m'  {— g ~j7s)i  where  p  =  r'  —  r.     Supposing  m 

to  be  74,000  miles  from  the  centre  of  Saturn,  and  Mimas, 
Enceladus,  and  Tethys  at  117,000,  150,000,  and  186,000 
miles  respectively,  and  taking  the  masses  as  proportionate  to 
their  volumes,  their  radii  being  taken  as  400,  400,  and  600 
miles,  we  find  for  their  relative  perturbative  effects  :  — 

Mimas 299 

Enceladus    .......         82 

Tethys          .         .         .  .         .         .no 

The  action  of  the  others  is  smaller  still.  Now 
the  major  axis  of  a  part  of  the  ring  which  has  a 
period  commensurate  with  that  of  Mimas  may  be 
found  from  the  formula  - 

r2  _  a^ 

77  ~  a? 

Kepler's  third  law.  Beginning,  then,  with  the 
simplest,  and  therefore  the  most  potent  ratio,  J, 
we  find  73,600  miles  for  the  major  axis  of  a  particle 


Saturn  and  its  System 


81 


whose  period  is  J  that  of  Mimas.  This  distance 
falls  almost  exactly  in  the  centre  of  Cassini's 
division. 

Proceeding  to  the  next  simplest  ratio,  \  of  Mi- 
mas's  period,  the  corresponding  distance  comes 
out  56,170  miles.  This  is  the  distance  from  the 
centre  of  the  planet  to  the  inner  edge  of  ring  B. 

Again,  \  of  the  period  of  Mimas  gives  46,370 
miles.  This  is  not  far  from  the  radius  of  the  inner 
edge  of  the  dark  ring.  So  much  for  the  action  of 
Mimas. 

The  major  axis  of  one  half  the  period  of  Encel-  ByEnceladus. 
adus  falls  without  the  system,  but  the  major  axis 
of  one  third  the  period  occurs  at  72,090  miles. 
This  is  not  far  from  the  inner  edge  of  Cassini's 
division.  But  the  striking  coincidence  with  Encel- 
adus  is  that  the  distance  corresponding  to  -f  of  his 
period  lies  at  81,400  miles,  or  at  Encke's  division. 

For  Tethys,  the  only  commensurable  ratio  is  \.    To  Tethys. 
This  makes  the  distance  fall  at  Cassini's  division. 

Thus  Mimas,  aided  by  Tethys,  has  been  the 
divider  of  the  rings  into  A,  B,  and  C ;  while  Encel- 
adus  has  subdivided  A. 

Not  less  interesting  mechanically  is  Saturn's 
satellite  system.  Eight  of  these  bodies  are  posi- 
tively known,  distanced  from  Saturn  and  diame- 
tered  as  follows  :  — 


Satellites. 


82  The  Solar  System 


RELATIVE   SIZE   AND 

POSITION   OF   THE   SATELLITES. 

No. 

Name. 

Diameter 
in  Miles. 

Distance  from  Saturn 
in  Miles. 

I. 

Mimas        .     . 

.       800 

....          117,000 

II. 

Enceladus  .     . 

.       800 

.      .      .      .          150,000 

III. 

Tethys        .     . 

.  I,2OO 

.      .      .      .          186,000 

IV. 

Dione         .     . 

.   1,100 

.      .       .      .          238,000 

V. 

Rhea          .     . 

.   1,500 

....          332,000 

VI. 

Titan          .     . 

•  3,500 

....          771,000 

VII. 

Hyperion   .     . 

.        500 

....       934,000 

VIII. 

lapetus       .     . 

.  2,000 

....    2,225,000 

Relative  ^  w^  ^e  seen  tnat  tne  largest  —  Titan  —  OCCU- 


the6  P^es  a  centra^  position  in  the  line.  This  might 
satellites.  seem  accidental  until  one  recalls  the  fact  that 
Jupiter,  the  largest  of  the  planets,  holds  the  same 
relative  place  in  the  solar  system  :  for  the  plan- 
etary system  tabulated  in  the  same  way  is  as 
follows  :  — 

SOLAR   SYSTEM. 

,,  ,.T  Diameter  in  Distance  from  Sun  in 

No.  Name.  MUg^  Millions  of  Miles. 

I.  Mercury     .  .  .     3,300  .....  36 

II.  Venus        .  .  .     7,630  .....  67 

III.  Earth         .  .  .     7,918  .....  93 

IV.  Mars          .  .  .     4,220  .....  141 
V.  Asteroids  .  .  .  10-500  .....  250 

VI.  Jupiter  .  .  .  86,500  .....  483 

VII.  Saturn  .  .  .  72,500  .....  886 

VIII.  Uranus  .  .  .  31,900  .....  1,782 

IX.  Neptune  .  .  .  34,800  .....  2,792 


Saturn  and  its  System  83 

With  the  hint  given  by  this,  at  least  singular, 
coincidence,  let  us  examine  the  other  satellite 
systems.  Two  others  available  for  comparison 
present  themselves,  —  that  of  Jupiter  and  that  of 
Uranus.  Jupiter's  system  is  this  :  — 

fj  A/  Diameter  Distance  from  Jupiter 

in  Miles.  in  Miles. 

V.  (Nameless).     .     .     100  ....  112,500 

I.  lo                ...  2,500  ....  261,000 

II.  Europa       .     .     .  2,100  ....  415,000 

III.  Ganymede.     .     .3,550  ....  664,000 

IV.  Callisto       .     .     .  2,960  ....  1,167,000 

Here,  again,  the  largest  body  fills  the  centre 
of  the  field. 

With  Uranus,  we  have  :  — 

jj  AT  Diameter  Distance  from  Uranus 

No-  Name-  in  Miles.  in  Miles. 

I.  Ariel  .  .  .  500  .....  120,000 

II.  Umbriel  .  .  .  400 167,000 

III.  Titania  .  .  .  1,000 273,000 

IV.  Oberon  .  .  .  800 365,000 

The  same  relative  agreement  of  position  and 
mass ! 

Now  consider  the  probability  that  this  coinci-    Position  of 
dent  arrangement  should  be  due  to  chance.     The    largest  mass* 
greater  mass  might  be  found  either  at  the  begin- 
ning, in  the   middle,   or  at  the  end  of  the  line. 
Take,  as  starting  point,  that  it  is  found  to  occupy 


84  The  Solar  System 

the  middle  of  the  line  in  the  Saturnian  system. 
The  chance,  if  chance  arranged  it,  that  it  should 
occupy  the  like  position  in  the  solar  system  is  one 
out  of  three,  or  two  to  one  that  it  did  not.  That 
it  should  also  do  so  in  the  Jovian  system  is  \  of  J, 
or  eight  to  one  against  it.  That  furthermore  the 
Uranian  system  should  show  the  same  is  \  x  J  x  i. 
In  other  words,  it  is  twenty-six  to  one  that  the 
largest  satellite  would  not  be  found  to  occupy  in 
all  the  same  position.  And  it  does.  Twenty-six 
to  one  in  betting  is  very  much  better  than  cer- 
tainty odds. 

Of  second  This  is  not  all.  Consider  the  four  systems 
more  carefully.  It  will  be  seen  that  the  second 
largest  mass  is  in  each  of  them  found  outside  the 
first  and  in  three  out  of  the  four  next  to  it.  In 
the  fourth,  it  comes  next  but  one.  Now  the 
chances  against  this  being  accident  are  much 
greater  than  for  the  first  coincidence ;  while  the 
chance  that  the  two  chances  should  occur  together 
as  they  do  is  the  product  of  both.  You  will  see 
that  we  are  getting  outside  any  chance  in  the 
matter  at  all,  and  have  come  face  to  face  with 
some  cause  working  to  this  end. 

Of  second       But  we  are  by  no  means  done  with  the  analo- 

maxima.          .  Tr  f          .  .         , 

gies  yet.  If  we  construct  a  curve  of  positional 
sizes,  we  discover  that  it  has  two  maxima,  not  one. 


Saturn  and  its  System 


A  second  lies  inside  the  first.  In  the  solar  system, 
our  Earth  occupies  this  place  ;  in  the  Jovian,  lo  ; 
in  the  Saturnian,  Tethys  ;  in  the  Uranian,  Ariel. 
Plotted  in  curves,  the  profiles  of  the  four  sys- 
tems show  a  striking  family  resemblance,  as  can 
be  seen  from  the  diagram  ;  and  from  what  we 
have  noted  of  the  probabilities  in  the  case,  we 
cannot  doubt  that  this  betokens  a  law  of  system 
development. 


JITII/E  ATTRACTIVE 

FORCE  OF 

PRIMARY  ON 

RCEST  SECONDARY 

Sun  on  Jupiter    t 

taken  as  unify 

M 


URANIAN      SYSTEM 


DISTANCE:  FROM   PRIMARY 
POSITION  OF  MASSES  IN  SATELLITE  SYSTEMS 
FIG.  XI. 


86 


The  Solar  System 


Inclinations 
of  orbits  to 
planet's 
equator  with 
increase  of 


A  second  point  connected  with  the  system  is 
the  relative  inclinations  of  the  orbits  to  the  plane 
of  the  planet's  equator.  The  inclinations  to  the 


distance  from   planet's  equator  of  the  rings  and  of  the  several 
planet. 

satellites  proceeding  outward  are  as  follows  :  — 


Same  in 

Jovian 

system. 


SATURNIAN    SYSTEM. 


Ecliptic. 
o       /      n 
28    10    22 
28    10    10 
28    10    10 
28    10    10 


Inclination  of  Orbit  to 

Planet's  Equator. 


Planet's  equator    .     . 

Rings  

Mimas 

Enceladus     .... 

Tethys 28  10  10 

Dione 28  10  10 

Rhea 28  10  10 

Titan 27  38  49 

Hyperion 27     4.8 

lapetus 18  28.3 


o  o 
o  o 
o  o 
o  o 
o  o 
o  o 

0  31 

1  5 


12 
12 
12 
12 
12 
12 

33 
34 


It  thus  appears  that  the  inclinations  of  the 
planes  of  the  orbits  to  the  plane  of  the  planet's 
equator  increase  as  the  distance  from  Saturn  in- 
creases ;  furthermore,  that  the  increase  is  regular. 
A  smooth  curve  represents  them  all. 

Now  let  us  turn  to  the  Jovian  system. 

The  inner  satellite,  or  Benjamin  of  the  family, 
moves  apparently  in  the  plane  of  its  primary's 
equator. 


Saturn  and  its  System 


JOVIAN    SYSTEM. 

Inclination  of  Orbit  Plane  to 
Planet's  Equatorial  Plane. 

I.  lo o°     o'    o" 

II.  Europa o°     i'     6" 

III.  Ganymede o°     5'     3" 

IV.  Callisto o°  24'  35" 

Here,  again,  the  inclinations  increase  as  we  go 
out,  and  the  smooth  curve  representing  them  is, 

INCLINATIONS    OF   SATELLITE    ORBITS    TO   PRIMARY'S    EQUATOR 


JOVIAN     SYSTEM 


!  Tethys 

;  M'l'mas     ;  ,0ione 


SATURN  IAN      SYSTEM 

•Hyper 


Titan 


flings  Enceladus 


FIG.  XII. 


Callisto. 


'lapetus 


when  reduced  in  scale,  almost  the  counterpart  of 
the  Saturnian. 

Clearly  some  force  has  operated  to  compel  the  Force  occa- 

,,.  .   .        ,          .  sioning  this 

satellites  to  travel  in  the  planet  s  equatorial  plane,  due  to  planet, 
and  this  force  has  emanated  from  the  planet,  since 
it  grows  less  potent  as  one  departs  from  him. 


88  The  Solar  System 

What  this  force  may  be,  we  shall  now  proceed  to 
ascertain. 

Combination  In  order  to  make  the  action  in  the  case,  com- 
plicated at  best,  as  understandable  as  possible,  I 
shall  begin  by  considering  what  causes  the  preces-, 
sion  of  the  equinoxes,  or  that  slow  rotation  of  the 
pole  of  the  Earth  round  the  pole  of  the  ecliptic. 

Effect  of  pull        Were  the  Earth  a  sphere,  its  axis  would  main- 

spherofcT5"7  tam  an  invariable  position  in  the  heavens,  since 
any  other  body  would  act  upon  it  as  if  all  its 
matter  were  collected  in  its  centre  ;  but  with  a 
spheroid  the  case  is  different.  We  may  consider 
the  equatorial  protuberance  as  a  ring  of  matter 
fastened  after  the  manner  of  a  life-preserver  around 
the  Earth's  waist.  Now  suppose  the  Earth  tilted 
up  from  the  line  joining  its  centre  and  the  centre 
of  the  attracting  body.  That  body  would  tend  to 
pull  the  nearer  part  of  the  ring  down  into  its  plane 
and  the  more  distant  portion  of  the  same  up  into 
the  same  plane,  and  the  result  would  be,  if  the 
Earth  were  not  rotating,  a  swing  round  an  axis  at 
right  angles  to  the  line  joining  the  centres  of  the 
two  bodies,  which  would,  after  a  few  oscillations, 
bring  the  equatorial  bulge  to  rest  in  the  orbital 
plane  of  the  outside  body. 

Upon  rotating       Now  suppose  the  Earth  to  be  rotating  at  the 

spheroid.  . 

time  the  pull  is  applied ;  then  the  simultaneous 


Saturn  and  its  System  89 

rotation  and  pull  entirely  alters  the  problem. 
From  being  a  statical,  it  becomes  a  kinematical 
one,  and  the  outcome  is  utterly  different  from 
what  we  might  expect.  Instead  of  bringing  the 
plane  of  the  equator  into  the  plane  of  the  ecliptic, 
it  swings  the  pole  of  the  equator  round  the  pole  of 
the  ecliptic  in  a  direction  at  right  angles  to  the 
pull,  and  opposite  to  the  rotation,  but  without 
changing  the  inclination  of  the  two  planes  perma- 
nently at  all.  If  the  axis  be  in  such  position  that 
the  pull  is  perpendicular  to  the  rotation,  no  change 
of  inclination,  even  temporarily,  occurs.  If  the 
axis  be  so  circumstanced  that  the  pull  is  at  any 
other  angle  to  it,  then  the  change  of  axis  being 
always  perpendicular  to  the  pull,  one  component 
of  the  change  rotates  the  axis  as  before,  the  other 
alters  its  inclination. 

Now  if,  as  is  the  case  with  the  attracting  bodies  Precession 
of  the  solar  system,  the  body  which  exerts  the 
pull  revolve  about  the  other,  either  really  or  vir- 
tually, the  axis  will  be  presented  to  the  force  under 
varying  angles.  The  axis  will  then  alternately 
approach  and  recede  from  the  pole  of  its  small 
circle  while  going  round  it.  But  at  the  end  of  its 
orbital  revolution  it  will  come  out  again  at  the 
point  on  the  celestial  sphere  from  which  it  started. 
And  this  will  happen  whether  the  orbit  be  a 


9O  The  Solar  System 

circle  or  an  ellipse.  Even  if  the  nodes  of  the 
ellipse  or  its  line  of  apsides  regress  or  progress, 
this  will  only  postpone  the  reentrance  of  the  curve 
into  itself  to  the  time  when  the  nodes  or  perihelia, 
or  both,  shall  have  completed  their  revolutions. 
No  perma-  No  permanent  change  in  the  inclination  of  the 

foaxfe11*1186  axis  to  tne  orbit  can  ever  result  from  tne  PUU  of 
a  second  body  upon  the  first's  equatorial  bulge. 

Since  action  and  reaction  are  equal  and  oppo- 
site, the  equatorial  protuberance  is  equally  impo- 
tent to  make  the  satellite  travel  permanently  in 
its  plane. 

Same  analyti-  This  appears  also  analytically  in  the  expressions 
for  the  effect  produced  in  the  line  of  nodes  and  the 
effect  upon  the  inclination,  the  former  having  in  ad- 
dition to  its  periodic  terms  a  term  which  increases 
with  the  time,  while  the  latter  has  no  such  term. 

Error  in  It  may  be  worth  pointing  out  here  an  error  which  has 

crept  into  Young's  excellent  text-books,  in  which  he  states 
that  "  Laplace  and  Tisserand  have  shown  that  the  equa- 
torial protuberance  of  a  planet,  due  to  its  axial  rotation, 
compels  a  near  satellite  to  move  nearly  in  the  equatorial 
plane."  Neither  Laplace  nor  Tisserand  has  ever  shown 
this  or  ever  could. 

Laplace  and  What  they  did  show  was  that  the  expression  for  the  per- 
turbative  action  of  the  equatorial  bulge  of  a  planet  denotes 
that  the  inclination  of  the  satellite  to  the  plane  of  the 
planet's  equator  remains  constant  under  the  action  of  that 


Saturn  and  its  System  91 

force.  Now  this  could  be  true,  either  because  the  force 
had  a  restraining  effect  to  this  end,  or  because  it  had  no 
effect  upon  the  inclination  at  all.  Laplace  jumped  to  the 
conclusion  that  the  first  was  the  case,  for  he  tells  us,  apro- 
pos of  Saturn  and  his  next  to  outer  satellite,  that  we  see 
"  that  Saturn's  action  can  retain  this  satellite  in  very  nearly 
the  same  plane ;  and  much  more  so  those  satellites  which 
are  inferior  to  it,  as  well  as  the  rings."  *  He  made  the  mis- 
take of  post  hoc  ergo  propter  hoc.  Tisserand  is  more 
guarded  when  he  says:  "Ainsi,  1'inclinaison  de  1'orbite 
d'un  satellite  sur  1'anneau  demeure  constante  et  toujours 
tres  petite  si  elle  Fa  ete'  seulement  a  un  moment  donneV' 
This  is  so ;  but  it  is  true,  not  because  the  force  has  an  ef- 
fect upon  the  inclination,  but  precisely  because  it  has  none. 
The  spherical  ellipse  found  by  Tisserand,  t.  iv.,  ch.  vi., 
to  represent  the  change  of  inclination  in  the  case  of  the 
satellites  of  Saturn,  is  the  curve  of  the  combined  preces- 
sions due  to  each  of  the  perturbing  forces,  the  equatorial 
protuberance,  the  ring,  the  sun,  and  the  other  satellites. 

Impotent  on  the  inclination  as  the  equatorial  Effect  of  tidal 
protuberance   is,   there   is  another   protuberance  C1 
which  is   not   so  impotent.      For  consider  what 
effect  the  tide-raising  force  of  an  outside  body 
would  have  upon  the  plastic  matter  of  another  ro- 
tating in  a  plane  tilted  to  the  orbital  plane  of  the 
first.     As  we  saw  in  Chapter  II.,  the  effect  would 
be  to  raise  two  bosses  or  ansae  in  the  equatorial 

1  See  Laplace,  Book  IV.,  §  26.  At  the  time,  Hyperion  was 
undiscovered  and  the  "  next  to  outer  satellite  "  in  consequence 
different. 


92  The  Solar  System 

plane  of  the  rotating  planet,  one  preceding  the 
position  of  the  tide-raising  body,  the  other  dia- 
metrically opposite. 

The  action  of  these  ansae  upon  the  attracting 
body  would  be  analogous  to,  but  in  one  vital  re- 
spect different  from,  that  of  an  equatorial  protu- 
berance. Like  that,  they  would  tend  to  alter  the 
position  of  the  axis  of  rotation  at  right  angles  to 
the  pull  upon  them,  but  the  pull  being  always 
backward  the  axis  is  constantly  solicited  forwards 
toward  the  attracting  body.  Consequently  the 
axis  of  rotation,  while  rotating  round  the  axis  of 
the  orbit,  would  generally  seek  the  satellite.  For 
the  force  here,  when  the  axes  are  perpendicular, 
is  at  its  maximum.  The  axis,  therefore,  continues 
to  tend  toward  the  orbital  plane. 

Same  Analytically,   in  this  case,  unlike  that   of   an 

equatorial  bulge  due  to  axial  rotation,  the  expres- 
sion for  the  change  of  inclination  contains  a  term 
dependent  on  the  time  and  increasing  with  it. 

This  term  causes  the  inclination  of  the  equato- 
rial to  the  orbital  plane  to  diminish  until  the  axis 
of  rotation  lies  in  the  plane  of  the  orbit. 


imr 


inclination  of       The  tidal  force  varies  as  — 7r,  approx.,  and  its 

satellite's 

orbital  planes  ,    c  .          A.  4?/zV2 

to  planet's        work  for  any  given  time  as     ^6   ,  approx. 

It  should  therefore  be  much  more  potent  upon 


Saturn  and  its  System  93 

a  near  satellite  than  upon  a  far  one,  and  we 
should  expect  the  line  expressing  the  action  to 
prove  a  curve  concave  to  the  axis  of  x,  when  the 
bodies  acted  on  are  not  too  dissimilar  in  size. 
Such  is  precisely  the  opposite  of  the  curve  the 
diagrams  present. 

Nevertheless  tidal  action  is  probably  the  cause 
of  the  law  of  inclinations  shown  in  the  orbits  of 
satellites  to  the  equatorial  plane  of  their  primary. 
But  it  would  seem  to  imply  that  the  farther  ones 
were  given  off  first,  and  very  much  the  first. 


JUPITER    AND    HIS    COMETS 

Jupiter  exem-      CHAOS  describes  Jupiter  at  present ;  the  seeth- 

plifies  chaos.    .  .  .  .  ,        _, 

ing  something  between  sun  and  world,  i  he 
planet  is  either  a  sun  in  its  senility  or  an  earth  in 
its  babyhood,  as  you  are  pleased  to  regard  it.  For 
the  one  state  passes  by  process  of  development 
into  the  other. 

A  semi-sun.  Viewed  as  a  sun,  it  lacks  little  except  light ; 
viewed  as  a  world,  it  wants  everything  except  that 
lack  of  luminosity.  It  is,  as  Virgil  described  an- 
other giant,  informe  ingens  cui  lumen  ademptum. 
Its  density  is  almost  exactly  that  of  the  Sun  itself. 
Either,  therefore,  its  bulk  is  chiefly  atmosphere 
round  a  kernel  of  planet,  which  is  Professor  Dar- 
win's conclusion,  or  its  smaller  mass  is  offset  by 
its  lesser  heat,  causing  a  like  condensation  of  the 
two  globes.  On  the  latter  supposition,  though  not 
luminous,  it  is  still  hot.  This  would  bear  out  and 
confirm  the  inference,  from  the  brick-red  color 
between  its  belts,  that  its  surface  is  at  a  red  heat. 
Almost  precisely  the  same  is  true  of  Saturn ; 
the  body  of  that  planet,  too,  being  a  faint  cherry 


Jupiter  and  his  Comets  95 

red.    Jupiter,  however,  we  see  much  the  better  of 
the  two,  and  we  may  describe  it  as  typifying  both. 

Both  are  bulky ;  their  masses  to  their  volumes 
being  such  that  their  mean  densities  are  respec- 
tively somewhat  greater  (1.2856)  and  somewhat 
less  than  water  (.69  Jo}.  Both  are  in  rapid  rota- 
tion ;  particles  on  their  equators  traveling  with 
speeds  comparable  with  their  orbital  velocities. 
Both,  in  consequence,  are  strikingly  flattened  into 
oblate  spheroids  whose  elliptic  curves  instantly 
strike  the  eye.  In  the  disks  of  both  we  look  only 
upon  atmosphere  and  cloud.  Lack  of  solidity, 
speed  of  self-movement,  cloudy  condition,  are  all 
so  many  signs  of  —  youth.  In  relative  —  if  not 
in  absolute  —  age,  both  planets  are  still  very 
young. 

Semi-suns  in  several  'senses,  the  two  planets 
are  three-quarters  way  in  their  journey  from  neb- 
ula to  world.  In  their  traits  both  more  closely 
resemble  the  Sun  than  the  Earth.  Indeed,  with 
the  trifling  exception  of  not  shining,  the  disk  of 
Jupiter  or  of  Saturn  bears  a  very  remarkable 
analogy  to  the  solar. 

In  a  large  telescope  and  in  good  seeing,  Jupiter    Ruddy  glow, 
is  a  color-picture  as  beautiful  as  it  is  marked.     A 
deep  pink  flush   suffuses  the  planet's  equatorial 
regions.     It  probably  betokens  the  parts  of  the 


96  The  Solar  System 

true  surface  that  are  laid  bare.  For  that  the  color 
is  due  to  the  selective  absorption  of  the  higher 
regions  of  the  planet's  air  is  negatived  by  the 
spectroscope,  which  shows  dark  bands  in  the  red. 
Rotation*  In  spite  of  its  enormous  bulk,  Jupiter  turns  on 
its  axis  with  such  speed  that  its  figure  is  flattened 
by  JTT.  Its  mean  time  of  rotation  is  gk  $$m.  We 
are  forced  to  say  its  mean  time,  not  because  the 
markings  cannot  be  accurately  timed,  nor  because 
of  any  change  in  the  planet's  moment  of  momen- 
tum, but  because  the  planet  does  not  rotate  as  a 
whole.  Different  parts  of  it  go  round  at  different 
rates.  Speaking  broadly,  the  nearer  the  equator 
the  greater  the  speed.  Between  the  equator  and 
latitude  30°  there  is  a  difference  of  six  minutes  in 
the  rotation  period.  But  the  several  belts  have 
each  its  own  period,  and  this  does  not  always 
accord  with  the  latitude.  In  addition,  particular 
spots  on  the  same  longitude  have  particular  spins, 
and  pass  by  each  other  at  speeds  from  seven  miles 
to  four  hundred  miles  an  hour.  White  markings 
travel  faster  than  dark  markings  close  beside  them. 
Thus  the  white  masses  around  the  great  red  spot 
drift  by  it.  The  spot  itself  has  changed  its  rate 
by  six  seconds  in  as  many  years.  It  is  pretty  evi- 
dent that  Jupiter  is  chaotic. 


Jupiter  and  his  Comets  97 

The   same  is  the  case  with  Saturn.      Stanley  Rotation  of 
Williams,  in  1893,  found  for  the  Saturnian  regions  " 
between  6°  N.  and  2°  S.,  io7'  i  3™,  and  for  those  be- 
tween 17°  N.  and  27°  N.,  io7'  15'".     Not  only  did 
latitudes  differ  in   rate,  but  different   longitudes 
went  each  at  its  own  pace. 

Something  similar  is  true  of  the  Sun.  At  the  Sun's 
solar  equator  the  spin  is  swifter  than  on  either 
side  of  it ;  and  the  rate  decreases  steadily  from 
the  equator  towards  the  poles.  Spots  near  the 
equator  go  round  in  25  days  (25.23  days),  spots  in 
latitude  30°  in  26^  days,  in  latitude  40°,  27  days, 
while  in  latitude  45°  they  take  fully  two  days 
longer  than  in  o°.  Now  Willsing  and  Professor 
Sampson,  of  Durham  University,  have  shown  that 
such  a  state  of  things  should  result  in  the  process 
of  condensing  from  nebula  to  star.  In  the  neb- 
ula, if  the  density  varied  from  place  to  place, 
which,  on  the  doctrine  of  chances,  would  certainly 
be  the  case,  the  several  parts  would  revolve  round 
their  common  centre  of  gravity  at  various  rates. 
As  the  nebula  condensed,  such  parts  as  held  to- 
gether would  tend  to  equalize  their  individual  mo- 
tions through  friction,  until  a  common  rotation 
was  brought  about.  But  this  would  consume  a 
long  time ;  in  the  mean  while,  the  equatorial  parts 
would  outstrip  the  others.  In  the  midst  of  the 


98  The  Solar  System 

equalizing  process  the  Sun,   Jupiter,  and   Saturn 
now  seem  to  be. 
Jupiter  has        Jupiter,  however,  has   progressed  beyond  the 

:loud  layers,   g^    in   that    the    outer   j^    of    hig   SUDStance 


have  cooled  down  enough  to  condense  into  cloud, 
due,  possibly,  to  the  planet's  smaller  mass.  On 
the  surface  of  the  Sun  things  are  still  kept  largely 
uniform  by  the  terrific  heat,  and  the  slower  rota- 
tion lets  us  perceive  no  latitudinal  layers.  On  the 
contrary,  Jupiter's  disk  is  striated  with  belts  of 
various  tone  and  tint,  according  almost  exactly 
to  the  parallels  ;  while  the  albedo,  or  relative 
brightness  of  the  disk,  62  per  cent,  of  absolute 
whiteness,  indicates  that  most  of  it  is  cloud. 
Jupiter's-  These  clouds  are  quite  unlike  our  terrestrial 

raised,  not"    ones-      Jupiter's  clouds  are  riot  Sun-raised,  but 
Sun-raised,     self-raised  condensations.     On  the  one  hand,  the 
Sun's  action  there,  only  ^V  °f  what  it  is  here,  is 
impotent  to  produce  the  effect  we  see  ;  on  the 
s  other,  the  cloud  zones  show  a  persistence  quite 
disregardant  of  the  Sun.     They  are  not  ephem- 
eral like  ours,   but  long-lived,  lasting  for  weeks, 
months,  and  even  years.     They  must,  therefore, 
be  Jove-caused. 

Disk  darkens  In  another  feature  Jupiter  resembles  the  Sun. 
Its  disk  darkens  to  the  limb.  None  of  the 
smaller  planets  do  this.  The  only  thing  capable 


Jupiter  and  his  Comets  99 

of  producing  such  effect  is  a  layer  of  atmosphere 
surrounding  the  disk  of  considerable  depth.  Ju- 
piter's atmosphere  is  dense,  and  the  absorption  to 
which  a  ray  of  light  would  be  subjected  in  pass- 
ing in  from  the  Sun  and  then  out  to  us  would  in- 
crease from  centre  to  circumference,  and  thus  dim 
the  edges  of  the  disk. 

Jupiter  has  two  families  of    bodies  connected  Comets 

associated 

with  him  ;  one  an  own  one  of  satellites,  the  other  with  Jupiter, 
an  adopted  one  of   comets.     With  his  satellites 
we   made  acquaintance  in  the  last  chapter;  we 
must  now  be  introduced  to  his  comets. 

Thirty-two  comets  circle  near  the  planet  and 
agree  in  the  following  distinguishing  character- 
istics :  — 

1.  Their  aphelia  hug  Jupiter's  orbit. 

2.  Their  ascending  nodes  occur  close  to  it. 

3.  Their  motion  is  direct. 

At  some  time  in  the  past,  therefore,  each  of  Association 
these  comets  must  have  passed  close  to  Jupiter, 
the  comet  and  the  planet  chancing  to  arrive  to- 
gether at  the  node.  At  that  epoch  the  comet 
must  have  suffered  great  disturbance  at  the  hands 
of  the  planet,  and  its  previous  orbit  have  been  rad- 
ically changed. 

D'Alembert,  accordingly,  suggested  that  Ju- 
piter had  captured  these  comets,  and  Laplace 


100 


The  Solar  System 


\jupjI5.?- 

^ — -     — 

FIG.  XIII.     JUPITER'S  FAMILY  OF  COMETS. 

extended  the  idea  ;  but  to  Professor  H.  A.  New- 
ton we  owe  the  most  important  research  in  the 
matter.  In  two  striking  memoirs  (1878  and  1893), 
he  showed  that  Jupiter  was  quite  capable  of  such 
capture  ;  but  he  started  with  the  assumption  that 


Jupiter  and  his  Comets  101 

comets  were  not  denizens  of  the  Sun's  domain,  so 
he  considered  only  parabolic  comets. 

We  now  know  that  all  comets  probably  that    Comets  all 

belong  to  the 

man  has  ever  seen  are  part  and  parcel  of  the  Sun  s    solar  system, 
retinue.     They   do   not    come   to  us  from  outer 
space,  but  are  stable,  if  erratic,  members  of  the 
solar  system.     In  the  light  of  this  fact,  we  may 
profitably  reconsider  the  subject. 

Picture  a  comet,   coming  in  to  the  Sun  from    Jupiter's 

sphere  of 

space,  to  pass  close  to  the  planet  in  its  journey,  influence. 
Within  a  certain  distance  of  Jupiter,  the  planet's 
pull  becomes  so  great  that  it  is  mechanically  more 
exact  to  regard  the  comet  as  obeying  Jupiter  and 
perturbed  by  the  Sun ;  and  if  the  approach  be 
very  close,  we  may  neglect  in  a  first  approximation 
the  Sun's  effect  during  the  passage.  This  region 
is  called  Jupiter's  sphere  of  influence,  and  is  of 
the  general  shape  of  an  ellipsoid,  whose  longest 
diameter  follows  the  planet's  path.  The  mean  ra- 
dius of  the  ellipsoid  is  three  tenths  of  the  Earth's 
orbit,  no  inconsiderable  distance,  and  the  extreme 
radii  differ  as  i  to  1.19. 

As  the  comet  is  traveling,  when  it  enters  the   Relative  orbit 

,  .  „,  about  planet 

planet  s   sphere  or    influence,    with  bun-imposed   an  hyper- 
velocity,  its  speed,  even  if  the  orbit  be  elliptic  of 
small  major  axis,  will  exceed  what  Jupiter  could 
cause.     It  will,  in  general,  approach  Jupiter  with 


IO2 


The  Solar  System 


Comet  accel- 
erated or 
retarded  ac- 
cording as  it 
passes  behind 
or  before  the 
planet. 


Jovian  hyperbolic  velocity,  and  its  relative  orbit 
about  the  planet  will  be  an  hyperbola.  Jupiter, 
therefore,  cannot  completely  possess  itself  of  the 
comet. 

The  general  equation  of  the  relative  motion  I 
shall  not  bother  you  with.  But  certain  deductions 
from  it  I  think  you  will  find  of  interest.  In  the 
first  place,  it  appears  that  the  comet  will  be  ac- 
celerated or  retarded,  according  as  it  passes  behind 
or  in  front  of  the  planet.  This  may  be  seen 
directly  from  the  consideration  that  if  it  pass  in 
front  of  the  planet,  it  accelerates  the  latter,  and 
since  action  and  reaction  are  equal  and  opposite,  it 
must  itself  be  retarded ;  contrariwise,  if  it  pass 
behind  the  planet. 

Suppose  now  the  comet  to  have  been  pursuing 
a  parabolic  path  before  the  encounter ;  then  the 
least  retardation  will  make  of  its  orbit  an  ellipse ; 
for  whether  a  body  move  in  an  ellipse,  a  parabola, 
or  an  hyperbola  is  a  question  simply  of  its  speed 
at  a  given  distance,  shown  by  the  well-known 
equation,  — 

*»  =„(*_!). 

\r      a) 


Into  hyper-       Similarly,  the  least  acceleration  will  throw  it  into 

bola  by 

acceleration,     an  hyperbola,  and  it  will  pass  out  of  the  solar  sys- 
tem, never  to  return. 


Parabola 
made  into 
ellipse  by 
retardation. 


Jupiter  and  his  Comets  103 

For  an  original  elliptic  orbit,  this  is  not  necessa- 
rily the  case.  A  comet  pursuing  such  a  path  may 
have  its  velocity  increased  and  yet  not  pass  out  of 
the  system.  In  many  cases,  however,  it  would  so 
result,  and  we  can  thus  perceive  how  comets  might 
come  to  us  from  other  systems  from  purely  inter- 
nal forces  there. 

The  maximum  effect  in  retarding  the  comet's  Jupiter's 

,          ,,  ,          T  maximum 

motion  occurs  when  the  comet  approaches  Jupiter  effect  in  short- 
in  such  a  direction  and  with  such  a  relative  speed  ^a^c^x™e 
as  to  be  turned  back  upon  the  planet's  path,  and 
to  leave  the  planet  in  the  direction  of  the  planet's 
quit,  with  a  relative  speed  equaling  the  planet's 
own.     It  is  then  left  stock-still  to  fall  into  the  Sun. 

Jupiter  can  do  more  than  this.  Though  to  Jupiter's  abso- 
leave  a  comet  stock-still  to  drop  into  the  Sun,  thus  effect.  ' 
shortening  the  major  axis  to  one  half  its  own,  is 
its  maximum  effect  in  the  way  of  contracting  the 
orbit,  its  power  over  the  comet  exceeds  such  limit. 
The  planet  can  actually  prevent  a  comet  bound 
round  the  Sun  from  attaining  its  object.  It  can 
cause  the  comet  to  make  itself  in  place  of  the  Sun 
the  goal  of  its  pilgrimage,  and  sweeping  round  the 
planet,  to  go  back  into  space  without  visiting  the 
Sun  at  all. 

Consider  the  hyperbola  the  planet  causes  the 
comet  to  describe.  What  the  planet  does  is  to 


104 


The  Solar  System 


Jupiter's  bulk  swing  the  incoming  asymptote  of  this  hyperbola 

limits  his  A ,  ,  .  . 

power.  through  a  certain  angle.     Clearly,  the  closer  the 

perijove  of  the  relative  orbit,  the  greater  this  angle 


tl 

V- 

A 

3&  '_    . 

B 

A 

X   / 

•>;S 

1 

The  comet's  direction  may  be  turned  from  OA  to  OB  ;  or  OA'  to  OB' ;  or  OA" 
to  OB",  according  as  it  approaches  along  OA,  OA',  or  OA'',  P  being  the  planet. 

FIG.  XIV.     RELATIVE  ORBITS. 


of  swing,  as  the  planet  gets  a  greater  pull  upon 
the  particle.  If  the  comet  were  not  coming  too 
fast  and  Jupiter's  own  body  did  not  get  in  the 
way,  the  comet  could  be  turned  straight  back 


Jupiter  and  his  Comets  105 

whence  it  came.  Practically,  Jupiter's  bulk  does 
get  in  its  way,  and  the  limit  of  the  planet's  power 
lies  below  such  direct  reversal ;  nevertheless,  it  is 
sufficient  in  many  positions  to  cause  the  comet 
to  sweep  round  and  dart  away  from  the  Sun 
with  a  speed  such  as  to  carry  it  beyond  the  Sun's 
control. 

The  planet's  greatest  effect  in  turning  the  comet 
is  shown  in  three  different  conditions  of  approach. 
The  comet  enters  along  the  unbroken  lines  and 
leaves  by  the  broken  ones. 

You  will  notice  that  Jupiter's  power  is  solely   Deflective 
one  of  deflection.     He  cannot  vie  with  the  Sun   } 
directly  in  a  tug  of  war ;  but  he  can  deflect  the 
comet  and  thus  use  the  very  speed  imparted  by 
the  Sun  against  the  Sun's  attraction.     It  is  like 
the  Japanese  jiu-jitsu,  or  scientific  wrestling,  of 
which  the  art  consists  in  so  adroitly  turning  an- 
other's strength  against  himself  as  to  make  the 
man's  own  momentum  cause  his  fall. 

Considering  the  case  in  this  wise,  we  shall  have   Triangle  of 
the  key  to  all  of  Jupiter's   control.     Form  a  tri-  vel< 
angle  of  velocities,  of  which   the  one  side  shall 
represent  Jupiter's  motion  in  amount  and  direc- 
tion, a  second  the  comet's,  and  the  third  the  rela- 
tive motion  of  the  one  body  about  the  other  ;  then 
draw  a  circle  with  the  last  for  radius  from  the 


io6  The  Solar  System 

meeting-point  of  the  planet's  and  comet's  true 
motions,  and  join  any  other  point  of  it  to  its  centre. 
This  second  radius  will  represent  the  outgoing 
asymptote  of  the  relative  orbit,  according  to  the 
planet's  pull,  while  the  line  joining  its  peripheral 
end  to  Jupiter  will  be  the  comet's  subsequent 
motion  in  amount  and  direction. 

From  this  you  will  perceive  that  the  comet's 
subsequent  career  depends  upon  the  actual  speed 
with  which,  the  angle  under  which,  and  the  near- 
ness to  which,  it  approaches  the  planet.  If  it 
creep  upon  the  planet  from  behind,  it  is  more 
likely  to  be  captured  than  if  it  meet  it  head  on ; 
and  if  it  be  traveling  slowly,  it  is  more  likely  to 
be  caught  than  if  it  were  going  fast. 

Direct  orbits  Any  one  of  many  things  may  happen.  If  it  pass 
grade/6  behind  the  planet,  its  actual  speed  is  increased, 
and  either  it  is  sent  clean  out  of  the  system,  or  it 
is  at  least  put  farther  from  capture  than  before. 
If  it  pass  before  the  planet  and  in  such  a  way  that 
its  relative  speed  about  the  planet  exceeds  the 
planet's  own  motion,  and  it  is  turned  round 
through  a  sufficient  angle,  it  may,  from  a  pre- 
viously direct  path  about  the  Sun,  be  diverted 
into  a  retrograde  one.  In  this  case,  it  will  com- 
1  monly  have  a  small  velocity  after  the  encounter 
and  retrograde  in  a  small  ellipse. 


Jupiter  and  his  Comets 


107 


FIG.  XV.     ACTION  OF  JUPITER. 

F represents  in  amount  and  direction  the  comet's  actual  velocity 
in  space.  V\  similarly  denotes  that  of  the  planet,  the  two  bodies 
meeting  one  another  under  the  angle  VO  V\.  VQ  will  then  re- 
present the  relative  motion,  in  amount  and  direction,  with  which 
the  comet  approaches  the  planet. 

The  action  of  the  planet  is  to  turn  the  relative  motion  of  the 
comet  through  an  angle,  say  AO£,  OA  representing  the  in-coming 
asymptote  of  the  relative  orbit,  OE  the  out-going  one.  EP  or  V 
will  then  represent  the  absolute  motion  in  space  of  the  comet 
after  the  encounter.  Similarly,  if  the  comet  passed  behind  the 
planet  and  was  turned  through  the  angle  AOI,  PI  would  be  the 
new  absolute  velocity  of  the  comet  on  leaving  the  planet. 


io8  The  Solar  System 

The  critical          It  however,  its  entering  speed  and  approach- 
ing angle,  which  we  will   call  o>,  are   such  that 

I        fj 

cos  w  <  -•—,  where  v  is  its  actual  velocity,  v^  that 

of  the  planet ;  then  its  relative  velocity ,  z/0,  can 
never  be  greater  than  vv  and  the  resulting  orbit 
never  can  become  retrograde.  This  angle  we  will 
call  the  critical  angle,  and  designate  it  by  the 
symbol  \. 

Now  w  we  can  calculate  for  each  of  the  comets 
of  Jupiter's  family  from  their  known  present  paths. 
Furthermore,  since  Jupiter's  only  effect  is  to  swing 
the  outgoing  asymptote  of  the  relative  orbit  round, 
v0  can  never  be  changed,  and  the  future  possible 
values  of  o>  have  a  superior  limit  o>',  which  they 
can  never  pass.  This  also  we  can  calculate. 
Doing  this,  and  calculating  also  the  value  of  x  for 
each  comet,  we  find  the  table  on  the  opposite 
page, 
w  and  «'  both  From  the  table,  it  appears  that  in  every  one  of 

aTcometsXofn    tne  comets  of  Jupiter's  family,  w  is  within  the 
Jupiter's  crit;cal  angle_ 

Furthermore,  that  c/,  the  maximum  value  which 
w  may  attain  under  the  perturbative  effect  of  the 
planet,  owing  to  the  swing  of  the  asymptotes  of 
the  hyperbolic  relative  orbit  of  the  planet,  is  also 
always  within  ^. 


Jupiter  and  his  Comets  1 09 


OO    w  sO  -i 


4-      d  »n  tx  d>  ood 

vO          t^\O  SO  sO  \D  O 


w' 

mum  val 
ible  for  w 


o'  rood  >-,' 
cottoxj- 


o  o  o«o 
\o  d-  vd  rood 
ro  N  •«-  ro  ro 


ax 
pos 


ro  00  O  00 
in  N  od  in 
m  ro  co  M 


O    «    •*•  O    «    « 


M    (>  •*  tx  O    in  roOO    O  tx  N    CxN    H  \O    «    rot^~  rovO    ro  O   CT>  -*OO    "•fH;fJlf>1-|O^     N 


-too  ooiOONNNiHi-iOON  O^O    t^OOO   row    IONOO    t^O    tx  rooO    O  vO   O    N    ro     ro 


Incli 
of  o 
ecl 


q>ONq\q  M  M\O  tvq  -*ONONN  in-^-m  t^oo  ^-fric>q«NooooNvqqcot>»qN    q^ 

+4-4-4-+++++++++++++++++4-+++++4-++++  " 


i  ro  tvoo   OO   «    C   OOfOO   -cooo   ooo   - 


'U 


no 


The  Solar  System 


o>  nearly 
ahnost  all"1 


Potential  rela- 

reVmaVinsOClty 
unchanged. 

Comets  of 


the 
disappear. 


Therefore,  of  the  comets  of  Jupiter's  comet- 
family,  not  only  is  none  now  retrograde,  but  none 
can  ever  become  so  unless  some  other  body  inter- 
fere with  it. 

A  singular  coincidence  characterizes  the  values 
°^  w  anc*  <•>'•  In  a^  but  two  cases,  <o  nearly  equals 
a/,  as  if  for  some  reason  o>  were  always  trying  to 
attain  this  maximum  as  a  condition  of  stable  equi- 
librium. In  ten  cases  out  of  twenty,  or  in  one 
half  of  the  whole,  the  approach  is  within  less 
than  J°. 

It  is  to  be  noticed  that  in  orbits  potentially 
retrograde,  the  potential  direct  velocity  is  also 
greatest  ;  so  that  both  on  the  score  of  retrograda- 
tion  and  of  greater  direct  velocity,  comets  pursuing 
such  orbits  are  more  subject  to  expulsion. 

In  course  of  time,  comets  possessing  a  high 
potential  velocity  must  be  weeded  out  of  the  sys- 
tem  .  for>  sooner  or  later,  they  must  meet  the 
planet  under  conditions  of  approach  which  con- 
vert their  high  potential  velocity  into  an  actual 
one.  This  will  happen  the  sooner  for  comets 
in  proportion  to  their  velocity  possibilities.  It 
therefore  will  occur  more  speedily  for  originally 
parabolic  comets  than  for  elliptic  ones  of  short 
period  ;  but  it  will  require  some  time  even  for 
them. 


Jupiter  and  his  Comets  1 1 1 

Either,  then,  Jupiter's  present  comet  family  has 
been  of  very  slow  growth,  and  each  comet  remains 
for  a  long  time  in  the  family,  or  it  is  made  up  only 
of  short-period  comets  drawn  from  the  immediate 
neighborhood. 

Now,  comets  appear  to  be  ephemeral  things,  Comets 
being  easily  disintegrated  into  meteor  swarms,  and  thi 
never  abiding  long  in  one  stay.  Thus  the  latter 
supposition  seems  on  the  face  of  it  the  more  likely. 
We  may  conclude  provisionally  that  Jupiter's 
comet  family  came  from  the  neighborhood. 

It  is  certain  that  Jupiter  has  swept  his  neighbor-  Jupiter  has 
hood  of  such  comets  as  do  not  fulfill  the  criterion  neighbor-8 
of  the  angle  x;  that  is,  of  all  the  comets  actually  or  l 
potentially  retrograde.     If  we  consider  the  comet 
aphelia  of  short-period  comets,  we   shall   notice 
that  they  are  clustered  about  the  path  of  Jupiter 
and  the  path  of  Saturn,  thinning  out  to  a  neutral 
ground  between,  where   there  are   none.      Two 
thirds  way  from  Jupiter's  orbit  to  Saturn's,  space 
is  clear  of  them,  the  centre  of  the  gap  falling  at 
8.4  astronomical  units  from  the  Sun. 

Let  us  consider   the  mean   comet ;  that  is,  a 
comet  having  the  mean  inclination  of  parabolic 
comets,  the  mean  perihelion  distance  of  the  comets 
of  Jupiter's   family,  —  such    being   the   distance  „ 
most  likely  to  disclose  them  to  us,  —  and  let  this 


Mean 

inclination  of 
comets : 
theoretical. 


112 


The  Solar  System 


mean  comet  have  successively  aphelion  distances 
from  Jupiter's  orbit  to  Saturn's. 

The  mean  inclination  we  may  take  either  as  the 
mean  of  comets  coming  to  us  from  all  parts  of 
space  indifferently  or  as  the  mean  of  such  para- 
bolic comets  as  have  actually  been  observed. 

If  we  suppose  the  inclinations  of  the  cometary 
orbits  to  be  equally  distributed  through  space, 
then  the  poles  of  the  orbits  will  likewise  be  strewn 
uniformly  over  the  celestial  sphere.  If  a  be  the 
angle  made  by  a  pole  with  the  pole  of  the  ecliptic, 
the  mean  inclination  of  the  poles  can  be  found  by 
multiplying  the  number  of  poles  at  any  inclina- 
tion, which  is  as  the  strip  of  surface  yielding  it, 
by  that  inclination,  and  then  dividing  the  integral 
of  this  for  the  whole  sphere  by  the  surface  of  the 
sphere.  The  strip  of  surface  at  any  inclination  a 
is  2  TT  r2  sin  a  .  da.  Whence  the  average  inclina- 
tion in  radians  is 


rv 

2vr2  sin  a.  a. 
Jo 

rv 

I     2  IT  r2  sin  a.  do. 
Jo 


or 


=  57u-3. 


Mean  mcima-       The  second  mean  inclination  or  actual  mean  of 

tion  observed.  . 

all  the  parabolic  orbits  observed  is  z  =  52  .4. 


Jupiter  and  his  Comets  113 

It  is  worthy  of  notice  how  near  the  two  are, 
showing  that  the  parabolic  comets  come  to  us, 
practically,  indifferently  from  all  parts  of  space. 

Calculating  w  and  x  for  the  successive  aphelia, 
we  find  that,  on  the  first  supposition,  w  passes  x  at 
8.4  astro,  units ;  on  the  second,  at  8.75  ditto. 

It  is  Jupiter,  then,  that  has  swept  this  space  of 
comets. 

Only  a  small  fraction  of  Jupiter's  comet  family  Family  larger 

...  i          r  tban  we  see- 

can  ever  come  within  our  ken ;  tor   any   comet 

whose  perihelion  lay  outside  of  two  astronomical 
units  must,  perforce,  escape  recognition.  Invisi- 
bility would  be  caused  both  by  the  comet's  dis- 
tance from  us  and  by  its  distance  from  the  Sun, 

J 
for  the  commotion  set  up  in  these  bodies,  as  they 

near  the  Sun,  is  chiefly  responsible  for  the  display 
they  make. 

The  family  undoubtedly  consists  of  many  more 
comets  with  greater  perihelion  distance. 

Jupiter  is  not  the  only  planet  that  has  a  comet- 
family.  All  the  large  planets  have  the  like. 
Saturn  has  a  family  of  two,  Uranus  also  of  two, 
Neptune  of  six  ;  and  the  spaces  between  these 
planets  are  clear  of  comet  aphelia  ;  the  gaps  prove 
the  action. 

Nor  does  the  action,  apparently,  stop  there. 
Plotting  the  aphelia  of  all  the  comets  that  have 


The  Solar  System 


been  observed,  we  find,  as  we  go  out  from  the 
Sun,  clusters  of  them  at  first,  representing,  re- 
spectively, Jupiter's,  Saturn's,  Uranus',  and  Nep- 


FIG.  XVI.     COMET  APHELIA. 


tune's  family ;  but  the  clusters  do  not  stop  with 
Neptune.  Beyond  that  planet  is  a  gap,  and  then 
at  49  and  50  astronomical  units  we  find  two  more 


Jupiter  and  his  Comets  1 1 5 

aphelia,  and  then  nothing  again  till  we  reach  75 
units  out. 

This  can  hardly  be  accident ;  and  if  not  chance, 
it  means  a  planet  out  there  as  yet  unseen  by  man, 
but  certain  sometime  to  be  detected  and  added 
to  the  others.  Thus  not  only  are  comets  a  part 
of  our  system  now  recognized,  but  they  act  as 
finger-posts  to  planets  not  yet  known. 

We  have  thus  examined  the  case  of  an  old 
planet,  —  Mercury  ;  of  a  middle-aged  one,  — 
Mars  ;  of  a  youthful  one,  —  Jupiter  ;  and  we  have 
ended  by  envisaging  the  yet  unchristened. 


VI 

COSMOGONY 

Present  the  AFTER  the  present,  the  past.  The  forces  that 
theCpast  °  we  have  f°und  to  be  moulding  the  system  to-day 
must  be  those  that  fashioned  it  earlier.  Given, 
therefore,  the  condition  at  the  moment,  if  we 
apply  to  it  the  forces  now  at  work  reversed,  we 
shall  get  the  condition  that  was. 

Similarly,  we  can  cast   its  horoscope  for  the 
future,  —  by  Taylor's  theorem. 

Unfortunately,  the  problem  is  so  complicated 
that  no  solution,  even  approximately  satisfactory, 
has   yet   been   obtained;  but   that   the   mystery 
baffles  us  renders  it  all  the  more  fascinating. 
Striking  reia-     In  the  solar  system,  as  we  find  it  to-day,  are 
solar  system  severa-l  remarkable  congruities  which  are  quite  in- 
dependent of  gravitation,  and  bespeak  a  cause. 

I.  The  central  body  is  much  larger  than   its 
attendants. 

II.  The  planets  move  in  orbits  nearly  circular. 

III.  They  travel  nearly  in  one  plane. 

IV.  And  in  the  same  sense  (direction). 
As  for  the  planets  themselves  — 


Cosmogony  117 


V.  Their  planes  of  rotation  nearly  coincide  with 
their  orbital  planes  (except  Uranus  and  Neptune). 

VI.  They  rotate  also  in  the  same  direction  that 
they  revolve,  counter-clockwise,  all  of  them  (except 
Uranus  and  Neptune). 

VII.  Their  satellites  revolve  nearly  in  the  planes 
of  their  primaries'  equators  (so  far  as  we  can  see). 

VIII.  And  in  the  same  direction. 

IX.  They  rotate  in  the  same  plane  (so  far  as 
we  can  see). 

X.  In  the  same  direction  (so  far  as  we  can  see). 
Immanuel  Kant  was  the  first  to  suggest  some-  Kant's 

thing  approaching  a  rational  explanation  of  this  hypothesis, 
very  curious  and  elegant  state  of  things.  He 
made  the  error,  however,  of  supposing  that  rota- 
tion of  the  whole  could  be  produced  by  collisions 
of  its  parts ;  but  no  moment  of  momentum  can 
be  caused  by  the  interaction  of  parts  of  a  system, 
since  internal  forces  occur  in  pairs  and  their  mo- 
ments round  any  line  are  equal  and  opposite.  We 
will  consider  this  in  detail  a  little  further  on.  La- 
place, who  appears  not  to  have  known  of  Kant's 
writing,  himself  some  years  later  developed  a 
somewhat  similar  theory,  but  with  more  mathe- 
matical foundation.  He  assumed  an  original  rota- 
tion and  got  the  credit  for  the  nebular  hypothesis. 
He  had  a  faculty  of  getting  credit  for  things 
which  was  only  second  to  his  ability. 


1 1 8  The  Solar  System 

Laplace's  To  account  for  so  orderly  an  arrangement  La- 

nebular  .  , 

hypothesis.       place  supposed  :  — 

a.  That  the  matter  now  composing  our  solar 
system  was  once  in  the  form  of  a  nebula. 

b.  That  this  original  nebula  was  very  hot,    a 
fire-mist. 

c.  That  it  possessed  initially  a  slow  rotation. 

d.  That  as  it  contracted  under  its  own  gravity 
and  thus,  from   the  principle  of  conservation  of 
moment  of  momentum,  rotated  faster  as  it  shrank, 
it  rotated  always  like  a  solid  body  with  the  same 
angular  velocity  throughout,  until  its  outer  por- 
tions, which  went  the  fastest,  came  to  go  so  fast 
that  the  centrifugal  tendency  overcame  the  cen- 
tripetal force  and  they  were  left  behind  as  a  ring. 

e.  That  this  ring  revolved  as  a  whole  until  it 
broke,  rolled  back  upon  itself  and  made  a  planet ; 
the  outer  parts  of  the  ring  having  the  swiftest 
motions,  the  resulting  planet  rotated  in  the  same 
sense  that  it  revolved. 

f.  The  planet  thus  formed  gave  birth  in  like 
manner  to  its  satellite  system. 

Physical  error      The  prestige  of  Laplace  gave  this  explanation 
hypothesis.8     a  mental  momentum  which  has  carried  conviction 
nearly  to  the  present  day.    But  it  is  erroneous  for 
all  that,  nor  can  it  be  made  to  work  by  any  addi- 
tions or  slight  alterations  as  some  text-books  will 


Cosmogony  1 1 9 


tell  you.  For  it  was  founded  on  what  it  has  now 
foundered  on  :  one  fundamental  mistake.  Laplace 
assumed  that  his  nebula  would  revolve,  as  he  saw 
the  air  around  the  Earth  to  revolve,  of  a  piece. 
But  he  forgot  that  friction  due  to  the  pressure 
alone  produces  this,  and  that  in  particles  moving 
freely  no  pressure  exists.  Under  the  pull  of  a 
central  mass  each  layer  of  the  nebula  would  re- 
volve at  its  own  appropriate  rate,  or  as  r~ *  So 
that  his  beautiful  explanation  of  the  agreement  in 
direction  of  the  rotations  and  the  revolutions  — - 
the  vital  point  of  the  theory  —  falls  to  the  ground. 

Faye  first  definitely  pointed  out  this  fatal  fal-    Faye's  nebu- 
lacy  in  Laplace's  hypothesis  in  1886,  in  his  "  Ori-    sis. 
gine  du  Monde,"  in  which,  after  reviewing  the 
previous  history  of  the  subject,  he  brought  for- 
ward a  new  theory  of  his  own,  both  elegant  and 
ingenious. 

He  begins  by  assuming  a  nebulous  mass  of  par- 
ticles, roughly  uniform  throughout,  but  with  local 
condensations.  He  supposes  this  nebula  cold,  for 
the  heat  can  be  trusted  to  come  of  itself.  With 
uniform  density  throughout,  the  speed  of  rotation 
would  also  be  uniform,  thus  giving  the  same  re- 
sult that  Laplace  got,  but  for  a  very  different  rea- 
son. In  a  spherical  mass  of  matter  of  uniform 
density,  a  particle  at  any  point  is  attracted  only 


1 20  The  Solar  System 

Force  origi-     by  the  sphere  within  it.     It  is  therefore  pulled  by 

nally  as  5r.  m        8rs 

the  force  -2  =  —?  =  8  r,  where  8  is  the  density. 

Since  the  force  is  thus  linear  it  may  be  resolved 
into  two  harmonic  motions  and  becomes  motion 
in  an  ellipse  with  the  acceleration  directed  to  the 
centre,  or  elliptic  harmonic  motion  whose  equa- 
tion is  expressed  in  vector  coordinates  :  — 

f  p  =  a  cos  (nt  4-  e)  +  b  sin  (nt  +  e\ 
whence   •<  p'=—  n\a  sin  (nt-}-  e)  —  b  cos  (nt-\-e}~\, 

[  p"=  —n2  [a  cos  (lit  +  e)  +  b  sin  (nt  -f  e}~\  —  —  u2p. 

The  form  of  the  ellipse  depends  upon  the  amount 
and  direction  of  the  initial  velocity  of  the  par- 
ticle. 

This  equation  shows,  first,  that  the  period  of 
rotation  is  the  same  for  all  the  particles  ;  and  sec- 
ond, that  the  angular  speed  in  such  different  neb- 
ulae is  as  the  square  root  of  their  densities. 
Subsequently       When  the  mass  has  practically  collected  in  the 

m  2jrf 

centre,  the  force  is  ^,  or  the  ordinary  law  of  grav- 
itation, giving  elliptic  motion  with  acceleration 
directed  to  the  focus,  or  elliptic  motion  par  excel- 
lence. 

At  any  intermediate  stage  of  the  process  he  sup- 

a 

poses  the  force  to  be  represented  byf=  a  r  -+-  ^> 
a  gradually  dying  out  and  ft  increasing  as  central- 
ization goes  on. 


Cosmogony  121 


Planets  given  off  under  the  first  state  of  things 
would  rotate  in  the  same  direction  in  which  they 
revolved ;  under  the  last  in  the  opposite  way. 
He,  therefore,  supposes  the  terrestrial  planets  to 
be  the  older  ;  the  outer  planets  the  younger  mem- 
bers of  the  system.  His  theory  makes  the  order 
of  birth  the  exact  contrary  of  Laplace's. 

More  recently  Lieutenant-Colonel  R.  du  Ligon- 
des1  has  evolved  another  cosmogony.  Ligondes's 
general  theory  is  ingenious,  but  to  me  not  convin- 
cing. His  first  point  is  unqualifiedly  good.  He 
starts  out  by  calling  attention  to  the  evidence 
offered  by  the  moment  of  momentum  of  the  solar 
system  upon  the  early  history  of  that  system.  He 
shows  that  to  produce  a  single  star  system  like 
ours,  the  original  motions  of  the  several  parts  of 
the  nebula  must  have  been  nearly  balanced,  the 
plus  motions  almost  canceling  the  minus  ones. 

It  now  becomes  of  interest  for  us  to  consider  Moment  of 

, .  .  ,.  ^  r  r  momentum. 

this  question.  Conservation  of  moment  of  mo- 
mentum is  as  fundamental  in  mechanics  as  the 
conservation  of  energy.  The  momentum  of  a 
body  is  its  mass  into  its  velocity,  and  the  moment 
of  momentum  is  this  mass-velocity  multiplied  by 
the  perpendicular  upon  its  direction  from  the  point 

1  Formation  Mecanique  du  Sysftme  du  Monde,  Gauthier-Villars 
et  Fils,  Paris,  1897. 


122  The  Solar  System 

or  line  around  which  the  moment  is  taken.  The 
moment  of  momentum  is  thus  twice  the  area 
swept  out  by  the  moving  body  about  the  fixed  one 
in  unit  time. 

When  two  bodies  collide,  the  amount  of  motion 
is  not  changed.  This  truth  is  the  result  of  experi- 
ment, and  was  first  determined  by  Newton.  If 
the  two  are  perfectly  inelastic,  they  move  on  after 
the  collision  as  one  mass  with  a  loss  of  kinetic 
energy.  If  perfectly  elastic,  they  rebound  in  such 
a  manner  that  not  only  the  amount  of  motion,  but 
the  kinetic  energy  remains  unchanged.  Now 
probably  no  bodies  are  perfectly  inelastic,  just  as 
no  bodies  are  perfectly  elastic.  In  the  case,  there- 
fore, of  the  bodies  in  nature,  while  the  amount  of 
motion  is  never  altered,  a  part  of  the  kinetic  energy 
is  lost  by  the  shock.  It  is  transformed  into  heat 
energy. 
Moment  of  Now  the  moment  of  a  velocity,  and  therefore  of 

momentum  ,        . 

constant.  a  momentum,  clearly  remains  constant  when  un- 
acted upon  by  any  force,  for  its  direction  continues 
the  same,  and  a  perpendicular  upon  it  from  any 
point  measures  out  the  same  area  in  the  same 
time,  as  the  perpendicular,  too,  is  constant. 

The  like  is  true,  if  it  be  acted  upon  by  a  force 
constantly  directed  to  the  same  point ;  for  in  that 
case  the  force  can  generate  no  velocity  except 
along  the  perpendicular  upon  the  line  which  repre- 


Cosmogony  123 


sents  the  body's  momentum,  and  therefore  cannot 
change  the  area  swept  out. 

When  two  bodies  collide,  therefore,  they  each 
bring  an  eternal  definite  amount  of  motion  to  the 
collision  ;  this  amount  is  unaffected  by  the  shock. 

Nor  can  the  mutual  attraction  of  the  two  bodies 
themselves  alter  it ;  for,  since  a  force  is  measured 
by  the  amount  of  velocity  it  can  generate  in  a 
given  time,  the  velocities  generated  must  be  as 
the  opposite  masses,  and  therefore  the  momentum 
produced  in  each  be  the  same. 

Let  m  and  mr  be  the  masses. 

Then  /w  t  =  m^m, 

and  fmit  =  vivmi, 

and  —  =  '—  j 

whence  in-^um  —  jnvmi 

or  Aa  =  —  Bb 

where  Aa  =  —  and  Bb  =  — 


FIG.  XVII. 


1 24  The  Solar  System 

Moreover,  it  is  directed  in  both  cases  along  the 
same  line.  Whence  its  moment  in  the  two  cases 
about  any  point  is  the  same  in  amount,  the  per- 
pendicular from  the  point  being  common  to  both, 
but  opposite  in  direction.  The  two  moments  thus 
destroy  one  another.  From  which  we  see  that 
the  internal  forces  of  a  system  are  unable  to 
change  the  moment  of  momentum  of  the  system. 
Similarly  they  are  incapable  of  having  created  it 
to  begin  with. 

The  present  moment  of  momentum  of  the  solar 
system  can  be  calculated.  It  is  found  to  be  nearly 
the  least  possible.  It  must,  therefore,  always 
have  been  so.  It  was  predestined  by  internal 
motions  to  make  a  single  star. 

So  far,  he  is  admirable,  but  from  this  point  I 
lose  him  ;  I  cannot  see  the  cogency  of  all  his  suc- 
ceeding steps.  They  lead  him  to  the  conclusion 
that  everything  is  as  it  should  be,  and  incidentally 
that  Jupiter  or  Neptune  is  the  oldest  planet, 
Uranus  the  next,  then  Saturn,  Mars,  the  Earth, 
Venus,  and  Mercury.  The  importance  of  the 
order  will  appear  shortly. 
Trowbridge's  With  regard  to  the  retrograde  rotations  of  the 

explanation  . 

of  direct  and  outer  planets  and  the  direct  rotations  of  the  inner 
ones,  Trowbridge  suggested  that  uniform  density, 
or  a  density  increasing  toward  the  centre,  would 


Cosmogony 


125 


account  for  it.  Suppose,  first,  the  density  uniform, 
or  nearly  so.  Then  the  inner  parts  of  the  mass 
that  went  to  form  the  planet  would  be  traveling 
fastest,  and  their  momentum  would  prevail  over 
that  of  the  outer  particles  and  give  a  retrograde 
rotation  to  the  whole.  Suppose,  however,  that 
the  density  increased  toward  the  inner  side  of  the 
mass.  Then  the  centre  of  inertia  would  be  so  far 
shifted  toward  the  inner  edge,  say  to  N,  that  the 
sum  of  the  moments  about  it  of  the  particles  from 
without  would,  owing  to  their  distance  from  it, 
surpass  that  of  those  within  and  a  direct  rotation 
result. 

The  attraction,  and  thence  the  velocities  in  the  Laws  of  force 
different  parts  of  the  nebula,  may  be  well  shown 
graphically. 

Faye's  laws  of  attraction 
in  condensing  nebula. 


x 
FIG.  XVIII. 


126 


The  Solar  System 


Faye's  equation  holds  only  when  a  and  £  are 
functions  of  r  as  well  as  of  t.  It,  therefore,  fails 
to  give  a  good  representation  of  what  occurs 
throughout  at  a  given  moment.  Furthermore, 
the  equations  do  not  hold  up  to  the  axis  of  y,  as  a 
discontinuity  occurs  so  soon  as  we  enter  the  cen- 
tral mass. 

A  better  picture  is  the  following,  somewhat 
changed  from  Ligondes.  As  the  matter  gets 
drawn  into  the  central  mass,  the  attraction  at  the 
outer  parts  of  the  original  nebula  grows  less  and 
less,  therefore  C  sinks  to  F,  and  the  successive 
curves  of  the  attraction  become  OC,  DD,  EE,  FF. 


Successive  curves  of  attrac- 
tion in  condensing  nebula. 
x=  radius  of  point. 
y  =  attraction  at  the  point. 


x 
FIG.  XIX. 


The  velocities  at   different  distances  follow  a 
similar  law. 

This  shows,  as  Ligondes  points  out,  that  there 


Cosmogony 


127 


is  a  maximum  velocity  somewhere  in  the  centre  of  Effect  on 
the  nebula,  which  degrades  on  both  sides,  so  that  r 
we  should  have  a  plan  of  velocities  for  outside 
and  inside  portions  of  the  nebula,  thus  :  — 


Maximum 
velocity. 


FIG.  XX. 


Supposing  the  density  either  the  same  through- 
out or  to  increase  toward  the  centre,  we  should 
have,  if  the  various  planets  were  formed  simul- 
taneously, a  retrograde  rotation  for  the  outer,  a 
direct  rotation  for  the  inner  ones. 

In  addition  to  the  ten  congruities  known  in  the   New  congrui- 
time  of  Laplace,  we  must  now  add  others  from   { 
knowledge  acquired  since,  to  wit :  — 

XL  All  the  satellites  turn  the  same  face  to 
their  primaries  (so  far  as  we  can  judge). 

XII.  Mercury  and  probably  Venus  do  the  same 
to  the  Sun. 

XIII.  One  law  governs  position  and  size  in  the 
solar  system,  and  in  all  the  satellite  systems. 


ace. 


128  The  Solar  System 

XIV.  Orbital  inclinations  in  the  satellite  sys- 
tems increase  with  distance  from  the  primary. 

XV.  The  outer  planets  show  a  greater  tilt  of 
axis  to  orbit-plane  with  increased   distance  from 
the  Sun  (so  far  as  detectable). 

XVI.  The  inner  planets  show  a  similar  rela- 
tion. 

Tidal  friction       Tidal  friction  explains  xi.  and  xii. ;  xiii.,  xiv.,  xv., 

explanation.     an(^  xyi-  are  as  vet  unexplained. 

Tidal  friction       Tidal  friction  would  account  for  xiv.,  but  only 

fails  with  A.  ,J_.         ,_,          ,,  L   ,,., 

axial  inclina-  on  the  supposition  that  the  outer  satellites  were 
given  off  first.  This  is  contrary  to  Faye's  theory, 
largely  so  to  Ligondes's,  and  is  not  championed  by 
any  other,  for  Laplace's  supposition  with  regard 
to  this  point  cannot  stand. 

Not  only  must  the  outer  satellite  have  been 
given  off  the  first,  but  very  long  before  the  next 
inner  one,  and  so  on  for  all ;  for  tidal  friction  is 
potent  as  the  inverse  sixth  power  of  the  distance. 
A  similar  objection  holds  against  the  attempt 
to  explain  the  increased  tilt  of  rotation  axis  to 
orbit  planes,  as  distance  from  the  Sun  increases  — 
both  for  the  outer  and  the  inner  planets.  This 
increased  tilt  with  increased  distance  is  well  worth 
particular  notice.  It  may  be  seen  in  the  follow- 
ing table. 


Cosmogony  129 


Inclination  of  Equator 
Planet.  to  Orbit-plane. 

Neptune -         HS0^) 

Uranus 98°(?) 

Saturn 27° 

•2° 

Jupiter 

Mars 25° 

Earth 23i° 

Venus °°(?) 

Mercury 

We  cannot  be  certain  of  Uranus  and  Neptune 
because  we  cannot  see  their  surfaces  well  enough 
to  be  sure  of  the  position  of  their  axes,  but  the 
planes  in  which  their  satellites  revolve  makes  the 
value  given  altogether  likely. 

The  tidal  friction  explanation  of  this  would 
make  Neptune  very  much  the  oldest  planet,  Ura- 
nus very  much  the  next  so,  and  so  on.  But  the 
explanation  is  not  satisfactory. 

Our  solar  system  has,  as  I  have  said,  a  very 
small  relative  moment  of  momentum ;   only  the  of 
one  thousandth   part  of   what  it    might  have  as 
exemplified  in  the  system  of  a  Centauri. 

One  supposition  will  account  for  the  small  mo-  ^^Oanbl0ef 
ment  of  momentum  of  the  system,  without  sup-  two  suns. 
posing  the  individual  motions  so  nearly  balanced 
at  the  start.     The  moment  of  momentum  would 
be  small  if  the  principal  mass  were  initially  col- 
lected in   the  centre  of  the  nebula.     Now  this 


1 3o 


The  Solar  System 


Physical 
condition  of 
meteorites 
sustains  this 
idea. 


Distribution 


would  be  the  case  if  the  present  system  had  been 
formed  by  the  collision  of  two  bodies.  For,  when 
dealing  with  such  masses,  the  elasticity  may  be 
considered  small,  and,  in  default  of  elasticity,  the 
matter  after  the  collision  would  be  found  chiefly 
near  the  scene  of  the  catastrophe  if  the  impact 
were  in  the  line  joining  their  centres.  The  col- 
lision in  space  of  two  bodies  happening  head  on 
is,  of  course,  one  of  which  the  chances  are  very 
small,  and,  were  it  not  for  another  fact,  might  be 
dismissed  from  reasonable  consideration. 

This  fact  is  the  present  constitution  of  the  un- 
attached particles  of  the  system,  the  meteorites. 
As  we  saw  in  a  preceding  lecture,  these  fragments 
betray  a  previous  habitat.  Their  character  shows 
that  they  came  from  the  interior  of  a  great  cooled 
mass  which  once  had  been  intensely  heated. 
They  are  therefore  proof  of  the  prior  existence 
of  a  great  sun,  and  that  they  should  be  now 
strewn  in  space  makes  the  theory  of  a  subsequent 
collision  far  less  improbable. 

If  such  a  collision  occurred,  the  fragments 
would  be  scattered  more  sparsely  according  to 
their  distance  from  the  scene  of  the  catastrophe, 
and  we  may  perhaps  assume  the  law  governing 
this  sparseness  to  be  the  curve  of  probability, 


132  The  Solar  System 

Then  the  probable  amount  of  matter  lying  be- 
tween x  and  x  +  dx  is  -^e—h***dx,  and  considering 

x  to  be  y,  and  y,  x,  we  have  similarly  for  the  prob- 
able amount  of  matter  lying  between  y  and  y  +  dy, 

*..-*•* 

The  probable  amount,  therefore,  in   the  rect- 
angle dxdy  is  —e-»(*+rtdxdy=~e~-**a>  where 

a—dxdy,  and  r  denotes  its  distance  from  the  ori- 
gin, or,  in  this  case,  the  centre  of  the  Sun. 

For  the  amount  in  a  ring  at  distance  r,  we  have 
a  —  r  dr. 

Effect  on  Consequently  it   is    evident  that  there  is  less 

relative  variation  in  the  density  with  the  distance 
as  one  goes  out.  A  fortiori,  therefore,  when  the 
planetary  masses  do  not  increase  in  like  propor- 
tion, the  two  ends,  the  outer  and  the  inner,  of  the 
strip  or  bunch  of  matter  that  went  to  make  each 
up,  vary  less  in  density  inter  se.  In  the  result- 
ant rotation,  the  speed  of  the  separate  particles 
counts  for  more,  relatively,  than  their  density, 
and,  in  consequence,  for  the  outer  planets  we 
should  get  a  retrograde  rotation  ;  for  the  inner,  a 
direct  one. 

Inner  planets       That  the  inner  planets  were  not  formed  early  in 
later  formed.  ^  svstem's  development  seems  pointed  at  pretty 


Cosmogony  133 


conclusively  by  their  several  masses.  Present 
mechanical  conditions  of  the  matter  inside  Jupi- 
ter's orbit  appear  to  point  to  the  pre-existent  in- 
fluence of  Jupiter  upon  it  before  birth.  Not  only 
do  the  amounts  of  matter  in  the  several  terrestrial 
planets  indicate  this,  but  the  lack  of  formation  of 
a  planet  in  the  gap  occupied  by  the  asteroids 
seems  well-nigh  conclusive  on  the  point. 

A  glance  at  the  axial  inclinations  of  the  outer  shown  by 
and  the  inner  planets   betrays   a   break   in   the  "rial  rotation, 
symmetry  of  their  arrangement.     Each,  taken  by 
itself,  evinces  a  gradual  righting  of  the  axis  as  one 
approaches   the    Sun.      This   appears    strikingly 
from  the  table  of  the  inclinations  of  the  equators 
of  the  several  planets  to  the  planes  of  their  orbits. 

This,  too,  seems  to  point  to  the  action  of  Jupi-  Jupiter's 
ter.     On  the  whole  it  appears  probable  that  Jupiter  j£|j°en  the 
existed  before  any  of  the  small  planets  within  its 
orbit,  and  profoundly  modified  them  prenatally. 

We  thus  come  to  a  conclusion  in  which  nothing  Conclusion, 
is  concluded  :  but  we  need  not  regret  that.  The 
subject  becomes  the  more  exciting  for  remaining 
yet  a  mystery.  We  now  know  of  relations  so 
systematic  and  singular  that  we  are  sure  some  law 
underlies  them,  and  it  is  rather  pleasant  than  oth- 
erwise to  have  that  law  baffle  our  first  attempts 
at  discovery. 


1 34  The  Solar  System 

Future  of  the       But  though  we  cannot  as  yet  review  with  the 

system. 

mind  s  eye  our  past,  we  can,  to  an  extent,  foresee 
our  future.  We  can  with  scientific  confidence 
look  forward  to  a  time  when  each  of  the  bodies 
composing  the  solar  system  shall  turn  an  un- 
changing face  in  perpetuity  to  the  Sun.  Each 
will  then  have  reached  the  end  of  its  evolution, 
set  in  the  unchanging  stare  of  death. 

Then  the  Sun  itself  will  go  out,  becoming  a 
cold  and  lifeless  mass ;  and  the  solar  system  will 
circle  unseen,  ghostlike,  in  space,  awaiting  only 
the  resurrection  of  another  cosmic  catastrophe. 


. 


Electrotyped  and  printed  by  H.  O.  Houghton  &>  Co. 
Cambridge,  Mass.,  U.S.  A. 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

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nl  9  hi 


APR1?197Z51 


REC'DLD    Ml  972  -I2AM89     - 
SEP  21  im  HA 


niversity  of  California^ 
Berkeley 


YB   Io984 


5 


